Evaluating Regulatory Reform: Banks' Cost of Capital and Lending

∗ Evaluating Regulatory Reform: Banks’ Cost of Capital and Lending

Anna Kovner† and Peter Van Tassel† May 2019

Abstract

We examine the effects of regulatory changes on banks’ cost of capital and lending. Since the passage of the Dodd-Frank Act, the value-weighted CAPM cost of capital for banks has averaged 10.5% and declined by more than 4% relative to non-banks on a within-firm basis. This decrease was much greater for larger banks subject to new regulation than for smaller banks. Over a longer twenty-year horizon, we find that changes in the systematic risk of bank equity have real economic consequences: increases in banks’ cost of capital are associated with tightening in credit supply and loan rates.

Keywords: Cost of Capital, Beta, Bank Regulation, Dodd-Frank Act, Banks JEL Classiﬁcation: G12, G21, G28

∗We are grateful to Charles Calomiris, Wilson Ervin, Stijn Van Nieuwerburgh, and Jeffrey Wurgler for discussing our paper and to Malcolm Baker, Mark Carey, Douglas Diamond, Fernando Duarte, Victoria Ivashina, George Pennacchi, René Stulz, and seminar participants at Chicago Booth, the Federal Reserve Bank of New York’s Effects of Post-Crisis Banking Reforms Conference, the NBER Risks of Financial In- stitutions Conference, the Federal Reserve Bank of Boston, and the Columbia/BPI Conference on Bank Regulation, Lending, and Growth for comments. We thank Davy Perlman, Anna Sanfilippo, and, particularly, Brandon Zborowski for outstanding research assistance. †Federal Reserve Bank of New York (e-mail: [email protected], [email protected]): The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors. 1 Introduction

Bank regulations have changed dramatically over the past twenty years. Deregulation in the late 1990s repealed long-standing laws separating investment and commercial banking activities, allowing for the rise of larger and more complex global banking institutions. The

ﬁnancial crisis followed nearly a decade later prompting the Dodd-Frank Act (DFA) which intensiﬁed regulation particularly for the largest banks.

In this paper, we estimate the net effect of changing regulations on banks’ cost of capital and systematic risk, as well as the impact on bank lending supply. We find that the banking industry’s value-weighted CAPM cost of equity capital soared to over 15% during the financial crisis, but then declined by 4.5% relative to non-banks after the passage of the DFA to

10.5%. At the same time, banks’ cost of capital has differentially increased by 1-2% in the post-DFA period relative to the late 1990s. Time-series changes in equity betas drive these results. Therefore, an additional interpretation of our findings is that post-crisis regulations have lowered systematic risk in the banking industry with the cost of capital for the very largest banks moving back toward its pre-deregulatory average. These changes matter for the real economy – when banks’ CAPM cost of capital falls, we find that banks expand credit supply and ease lending terms to borrowers.

Rather than focus on the impact of a single regulation, such as changes to capital standards, our approach acknowledges that banking regulations are endogenous and often change simultaneously. For example, consider the DFA. A priori, it is unclear what effect the DFA should have on the cost of capital for banks. The DFA increased effective capital requirements, established recovery and resolution frameworks, and introduced new liquidity requirements and leverage constraints, particularly for the largest banks. These different regulations have varied and potentially opposing effects on the cost of capital. Safer banks may be expected to have a lower cost of capital, but any rollback in perceived government guarantees

1 may increase the cost of capital.1 Liquidity requirements may reduce the risk of bank runs

but change banks’ proﬁtability margins.

The ﬁrst contribution of this paper is to separate the net eﬀect of regulatory changes

from other factors impacting the cost of capital such as interest rates and the business cycle.

We do this by estimating a variety of difference-in-differences specifications that compare

changes in the cost of capital for banks to non-banks across periods separated by key dates in

bank regulation. These regulatory changes are: Gramm-Leach-Bliley Act (GLB) (November

1999), Financial Crisis (January 2007), Supervisory Capital Assessment Program (SCAP)

(May 2009), and DFA (July 2010). The results highlight the importance of examining

changes to banks’ cost of capital relative to other ﬁrms and across time periods, rather than

only focusing on pre-crisis versus post-crisis changes for banks (as in Sarin and Summers

(2016)).

To conﬁrm that we are capturing changes to bank regulation and not other factors like

interest rates, we take several approaches. First, we ﬁnd similar results when we compare

banks to non-bank ﬁnancial intermediaries, a control group of ﬁrms with business models

that are similar to banks but that are not directly aﬀected by changes to bank regulation.

Second, we compare changes for banks more aﬀected by regulation to those less aﬀected

(large versus small). This analysis is particularly relevant when estimating changes around

the passage of the DFA. Since the DFA, we ﬁnd that the CAPM cost of capital for the

largest banks has diﬀerentially declined by 3-4% relative to post-crisis highs and by 0-2%

relative to the pre-GLB period. We also look within the largest US banks and study the

staggered implementation of stress tests for banks with more than $50 billion in assets (as

1Even the impact of changes in capital requirements on the cost of equity is debated. On one hand, bankers argue that equity is more expensive than debt, so holding more equity increases the cost of capital with negative implications for growth and lending (see the discussion in Admati et al.(2014)). On the other hand, academics often contend that lower leverage should lower the cost of equity capital, leaving banks indiﬀerent to their capital structure in the absence of tax advantages for debt and other frictions (Modigliani and Miller 1958).

2 in Flannery et al.(2017)) and find a differential decline in the CAPM cost of capital for the very largest stress-tested banks. Overall, the results suggest that the net effect of the DFA regulations was to lower the cost of capital for the largest banks, outweighing countervailing effects such as the potential for lower expectations of government insurance in the post-crisis period (Atkeson et al. 2018).

Finally, we conﬁrm our results by repeating our main regression speciﬁcations using multifactor cost of capital estimates that incorporate interest rate factors (Schuermann and Stiroh

2006), CAPM cost of capital estimates with a time-varying equity risk premium (Cochrane

2011), log changes in CAPM betas that difference out the equity risk premium, and asset betas that de-lever bank stock returns (Baker and Wurgler 2015). Across measures, we consistently find a decrease in the cost of capital for the largest banks since the passage of the DFA. By some measures, we also estimate that the largest banks’ cost of capital has differentially fallen post-DFA relative to the levels that prevailed in the late 1990s.

Our approach adds a different perspective to the set of papers that study the effect of individual regulations on stock returns. For example, Baker and Wurgler(2015) show that the low-risk anomaly holds for bank stocks with the implication that higher capital requirements resulting in lower leverage and lower CAPM betas may not decrease the realized cost of equity capital. Gandhi and Lustig(2015) and Kelly et al.(2016) examine implied government guarantees using size-sorted bank portfolios and equity option prices and find that too-big- to-fail subsidies decrease the cost of capital for the largest banks and for the financial sector.

In contrast to studies that rely on a portfolio-based approach, our panel-based approach accounts for how changing bank business models and the changing composition of regulated banks aﬀects the results. For example, this allows us to control for banking industry consol- idation around the ﬁnancial crisis and the increase in non-interest income over the sample period. In addition, this paper also adds to the literature that studies how market measures

3 such as Tobin’s q are related to bank characteristics such as asset size, the value of intangibles, and the composition of bank assets (Minton et al.(2017), Calomiris and Nissim(2014),

Huizinga and Laeven(2012)). For example, Calomiris and Nissim(2014) emphasize the changing market perception of the value of bank intangibles and leverage for market-to-book ratios. Similar to Calomiris and Nissim(2014), we ﬁnd evidence of time-varying relation- ships of some bank characteristics. Speciﬁcally, the association between risk-weighted assets

(RWA) and bank betas is strongest during the ﬁnancial crisis, explaining most of the post-

ﬁnancial crisis fall in the CAPM cost of capital for the banking industry in aggregate. This result appears to be driven by loans and loan commitments, particularly real estate loans.

Even with the inclusion of time-varying controls, however, there is still a signiﬁcant decline in the post-DFA cost of capital for the largest banks, consistent with the interpretation that regulation has lowered systematic risk.

The ﬁnal contribution of the paper is to document that these changes in banks’ CAPM cost of capital matter for the real economy, thus relating our analysis to the real eﬀects of bank regulation. We hypothesize that banks’ CAPM cost of capital matters because the

CAPM is used in practice by managers, investors, and lawyers (Graham and Harvey(2001),

Berk and van Binsbergen(2016), Gilson et al.(2000)). For example, for non-ﬁnancial ﬁrms, investment is sensitive to the cost of debt and the weighted average cost of capital (Philippon

(2009), Gilchrist et al.(2013), Frank and Shen(2016)). Bank managers anecdotally use cost of capital estimates to allocate capital across divisions and bank CEOs cite the need to meet investors’ return on equity targets as documented in annual reports and in bank executive compensation packages (Pennacchi and Santos 2018). To our knowledge, this study is the

ﬁrst to establish an empirical relationship between bank-level CAPM cost of capital estimates and bank lending supply.

We establish this link using conﬁdential bank level survey response data from the Senior

4 Loan Oﬃcer Opinion Survey (SLOOS), a survey used to measure banks’ willingness to lend that allows us to separate credit supply eﬀects from demand (Lown and Morgan(2006),

Hirtle(2009), Bassett et al.(2014), DeYoung et al.(2015)). We find that changes in the cost of capital are associated with changes in the supply and the pricing of credit. This result holds in aggregate for the panel of surveyed banks as well as in the cross section after controlling for changes in the risk-free rate, business cycle variation, and bank-level stock market returns to account for firm-specific shocks. When banks’ CAPM cost of capital increases, bank managers tighten loan standards and increase loan spreads. Through this channel, regulations that lower CAPM costs of capital after DFA are passed through to the real economy.

2 Estimating the cost of capital

2.1 CAPM cost of capital

The cost of capital reﬂects the expected return of equity investors as well as the time value of money as captured by the risk-free rate. Empirically, expected stock returns are not observed.

Instead, we must rely on economic or statistical models to estimate expected returns. As a result, any test regarding the cost of capital is a joint test of the null hypothesis and the model that is used to estimate expected returns (Fama 1970). We use the CAPM for our baseline cost of capital analysis, but conﬁrm our results are robust to other measures in

Section6. Our focus on the CAPM is motivated by its widespread use in practice. The relevance of this approach is evident in section5 where we ﬁnd the CAPM cost of capital aﬀects bank lending supply

5 We deﬁne our estimate of the CAPM cost of capital as,

CAP Mi,t = Rft + βi,t · µ. (1)

The ﬁrst term is the risk-free rate Rft. The second term is a time-varying CAPM beta

2 βi,t. The last term is the equity risk premium µ, which we assume is constant. We set

the risk-free rate to the three-month Treasury bill rate and the equity risk premium to 8%,

the average CRSP value-weighted excess return from 1926 to 2017. The betas are estimated

from one-year rolling regressions of ﬁrm-level daily excess returns onto market excess returns.

The market return is the CRSP value-weighted return obtained from Ken French’s website.

The estimates are ex-ante betas in the sense that each month the beta is computed using

lagged daily data over the previous 252 trading days.

A number of alternative choices can be made when estimating betas. For example, to

name a few methods from a large literature, betas can be estimated from ﬁve-year rolling

regressions with monthly data, one-year rolling regressions with daily data, or directly from

volatility and correlation estimates.3 Betas may also use lagged, centered, or forward data

depending on the application. Given our interest in how the cost of capital has varied

over time, we prefer using daily data (252 observations per year) to deliver more precise

and less biased estimates in comparison to slow moving estimates from monthly data (60

observations per ﬁve years). We use an ex-ante (lagged) approach in order to approximate

2Betas can be estimated precisely with high frequency data. In contrast, the equity risk premium is notoriously diﬃcult to estimate. Even with a constant risk premium and log-normal returns, it would take over forty years to estimate the equity risk premium with a standard error of 3% (Merton 1980). This imprecision dominates the uncertainty in estimating expected returns in factor model settings (Fama and French 1997). Empirically, Welch and Goyal(2007) ﬁnd that many models under perform the historical mean and are unstable out of sample. Based on this observation and for simplicity, we assume the equity risk premium is a constant equal to the historical mean in our baseline analysis. We relax this assumption in Section6. 3For example, see Scholes and Williams(1977), Fama and French(1997), Ang and Kristensen(2012), Frazzini and Pedersen(2014), and Baker and Wurgler(2015).

6 manager estimates of their cost of capital.

An implication of this approach is that we rely on the time-series and cross-sectional

diﬀerences in betas to identify changes in the cost of capital. If we assume the CAPM

holds and the equity risk premium is roughly constant over our regulatory periods, time

variation in betas will reﬂect how the cost of capital is changing for banks relative to other

ﬁrms, even if there is large uncertainty surrounding the level of the cost of capital itself.

Of course, the well-documented low-risk anomaly and time-variation in discount rates pose

challenges for this interpretation (Black et al.(1972), Cochrane(2011), Frazzini and Pedersen

(2014), Baker and Wurgler(2015)). Stocks with high (low) equity betas have historically

earned lower (higher) returns than predicted by the CAPM and variation in price-dividend

ratios indicate that either discount rates or cash ﬂow growth rates are varying over time.

To account for this, Section6 explores the robustness of our results to alternative cost of

capital estimates including multi-factor models, the CAPM with a time-varying equity risk

premium, and the weighted average cost of capital (WACC).4

2.2 Sample selection and deﬁnition of banks

We use CRSP, Compustat, and regulatory data from call reports and Y-9C ﬁlings from

March 1996 to December 2017 when estimating the cost of capital and for panel regressions

with bank characteristics. We estimate the cost of capital for all CRSP ﬁrms with share

codes 10 or 11 that are traded on the NYSE, NASDAQ, or AMEX. Later in the paper we

also estimate asset betas by merging quarterly Compustat data onto monthly CRSP data

using the most recent observation that was announced prior to the start of the month (based

on RDQ date). We ﬁlter observations from this dataset with missing cost of capital estimates

4In comparison to the CAPM, multi-factor models have been criticized for poor out-of-sample performance and for data snooping (Linnainmaa and Roberts(2016), Harvey et al.(2016)) . Larger models also have the disadvantage that they are less likely to be used by managers.

7 or missing Compustat asset data as well as observations with share prices that are less than

one dollar. The resulting sample includes a panel of 1,111,127 ﬁrm-month observations.5

Deﬁning banks within this sample is not straightforward. Limiting banks to depository

institutions in SIC code 60 would exclude ﬁrms that became bank holding companies after

the financial crisis in 2009. These firms are subject to financial regulation that is a key object

of interest in this analysis. We therefore expand our deﬁnition to include both ﬁrms that

are depository institutions (SIC code 6020-6036) as well as ﬁrms that have an RSSDID (the

unique identifier assigned to financial institutions by the Federal Reserve) between the first

and the last dates when regulatory assets from Y-9C ﬁlings are within 10% of total assets

from Compustat. Firms that fulﬁll either of these criteria in month-t are identiﬁed as banks

by the binary variable Banki,t. We identify RSSDIDs using the FRBNY RSSDID-Permco

crosswalk, which matches banks between Compustat and regulatory reports using name,

city and state, and financial variables.6 Of the 11,961 firms in the sample, 1,415 firms are

identified as banks throughout the sample while 34 firms are identified as banks for only

part of the sample, including Metlife, Goldman Sachs, and Morgan Stanley. Because we

include savings and loans in our definition as banks, and these firms only file call reports

after 2012:Q1, there are fewer banks with regulatory data than there are total banks. The

result is a sample containing 99,049 bank-month observations for banks with regulatory data

5In the event that firms issue multiple securities, we obtain unique firm-month observations by retaining the PERMCO-date pairs for the security (PERMNO) that has the largest market capitalization each month. Our use of the most recent quarterly accounting data from Compustat is similar to Hou et al.(2014) and Adrian et al.(2015) who form portfolios based on recent quarterly earnings data. This differs from Fama and French(1993) who form portfolios annually. 6SIC codes are obtained with descending priority from Compustat historical, Compustat header, CRSP historical, or CRSP header data depending on availability following the procedure described in Adrian et al. (2015). RSSDID-Permco matches are based on the FRBNY crosswalk as of 2016q4. This definition of banks differs from an entirely SIC code or NAICS driven approach. For example, 24 companies with SIC code 6099 (functions related to depository banking) are not coded as banks at some point in our sample. This subset includes some of the credit card companies that do not have an RSSDID or regulatory assets that match Compustat data (i.e. Mastercard, Visa). At the same time, 13 companies with an SIC code beginning with 62 are coded as banks in our analysis (i.e. Goldman Sachs, Morgan Stanley). We exclude AIG from the sample.

8 when all regulatory variables are available as compared to 142,189 bank-month observations for the cost of capital.

3 Measuring changes over time in the cost of capital

We compare changes in the cost of capital across time periods in which bank regulations changed from 1996 to 2017. The periods are:

1. Basel I: Pre-period (March 1996 to October 1999)

2. GLB: The Gramm-Leach-Bliley Act (November 1999 to December 2006)

3. Crisis: The Financial Crisis (January 2007 to April 2009)

4. SCAP: The Supervisory Capital Assessment Program (May 2009 to June 2010)

5. Dodd-Frank: The Dodd-Frank Act (July 2010 to December 2017)

We deﬁne break points as the month of the passage of the relevant banking law. Results are similar if we vary the time periods within a few months to capture anticipation of the passage of the law. Figure1 plots the monthly value-weighted average cost of capital for banks with dashed-horizontal lines at the means of the diﬀerent regulatory time periods.

These simple averages do not control for diﬀerences in the composition of the panel nor

firm characteristics, and confidence intervals around these means would not account for the the fact that the observations are not independent (neither over time nor within firm). We therefore estimate the following specification to see how the cost of capital has changed over time:

CAP Mi,t = α + β1GLBt + β2Crisist + β3SCAPt + β4Dodd-F rankt + ei,t (2)

where CAP Mi,t is the estimated CAPM cost of capital and GLBt, Crisist, SCAPt, and

Dodd-F rankt are binary variables equal to one during the periods deﬁned above. The

9 omitted pre-period begins twenty years ago in 1996 and thus is characterized by the Basel I regulatory regime.

The estimated coefficient for each time period is the difference between the average cost of capital in that time period relative to the pre-period, whose value is captured by the constant term. The null hypothesis is that all β are equal to 0 – meaning that there have not been any changes to the CAPM cost of capital over time and, as a result, that regulatory changes have not changed the cost of capital. We estimate the specifications both on a value-weighted and equal-weighted basis to understand how the cost of capital is changing in aggregate and for the average company in the panel. Standard errors are clustered by firm and by month.

Results are similar if the analysis incorporates earlier data (back through 1986), however, we focus on the more recent time period to have consistency in the regulatory data, which becomes available for all ﬁelds used in the analysis starting in 1996:Q1.

3.1 Diﬀerence-in-diﬀerences across industries

We estimate our first difference-in-differences regressions by adding a bank indicator variable that is interacted with each of the time period dummies,

CAP Mi,t − Rft = α + β1GLBt + β2Crisist + β3SCAPt + β4Dodd-F rankt

+ρBanki,t + δ1Banki,t · GLBt + δ2Banki,t · Crisist + δ3Banki,t · SCAPt (3)

+δ4Banki,t · Dodd-F rankt + ei,t

This speciﬁcation nets out the risk-free rate Rft and allows the cost of capital to change diﬀerently for banks and non-banks around the time periods when bank regulation changed.

When we estimate δ that are diﬀerent from 0, changes to the cost of capital for banks relative to the pre-period are diﬀerent from that for non-banks.

This approach allows us to mitigate issues with the changing composition of the panel

10 over time by estimating the same regression absorbing firm fixed effects αi that replace

the constant α. The changing panel would otherwise present an issue around the financial crisis as a number of very large banks and broker dealers exit the sample due to mergers or bankruptcy while a number of very large broker dealers and credit card companies become bank holding companies. Beyond the crisis, there are also changes in the panel throughout the sample due to private firms entering by going public and public firms exiting as a result of mergers and acquisitions. In addition to the changing panel, we also begin to control for

firm characteristics by narrowing in on the effect of changing leverage. Some specifications include controls for Leveragei,t which is defined as total debt divided by the market value

of assets (total debt plus the market value of equity). For banks we add total deposits

to total debt when calculating leverage because the Compustat measure of total debt does

not include deposits. In unreported regressions, we include 3-digit SIC code ﬁxed eﬀects as

controls and expand the the deﬁnition of banks to include all ﬁrms that have RSSDIDs, and

results are similar.

3.2 Top ﬁrms

While the diﬀerence-in-diﬀerences regressions highlight the change in the cost of capital for

banks relative to other ﬁrms, they potentially conﬂate the impact of changing regulation

with other sources of time variation in the cost of capital. The cost of capital for the very

largest firms in any industry may be different from that of smaller firms, for example, as a

result of diﬀerences in systematic risk, market beliefs about implicit government support, or

an association between ﬁrm size and market power.7 In the bond market, Hale and Santos

(2014) ﬁnd that all large ﬁrms pay lower rates for bonds, and the very largest banks pay

7While large banks may be better diversified, diversification may not result in reduced risk to the extent that it facilitates greater leverage or riskier lending (Demsetz and Strahan 1997). As a result, large and diversified banks may still be exposed to the economy in general, resulting in high systematic risk which is the only risk priced in the CAPM.

11 diﬀerentially lower rates than non-banks. Further, the relationship between size and expected returns can change over time. To better understand the impact of regulation targeted at the largest banks, we thus need to ensure that we diﬀerence out changes over time in the cost of capital by size so we do not attribute those changes to changes in bank regulation.

To build a time series of large banks, we look more closely at the subset of banks most aﬀected by post ﬁnancial crisis regulatory changes, banks with more than $50 billion in assets.

Banks with more than $50 billion in assets are approximately the twenty largest banks in the US, so we create a dummy variable (“Top”) to capture the largest twenty firms by total assets within each industry at each point in time. We define industries by SIC code using the twelve industry portfolios on Ken French’s website and split financials into banks and non- bank financials using the definition described before. This gives us a measure that we can use over a long time series and across industries. We repeat the analysis from equation3 adding interactions between our coefficients of interest and the Top dummy variable. A significant interaction between Top, time period, and bank indicates that the difference between Top banks and smaller banks is different than the difference between Top non-banks and non-Top non-banks in the current period relative to the pre-period.

3.3 The role of bank characteristics

In order to understand how changes to bank business models, capital, and liquidity are aﬀecting their cost of capital, we zoom in on regulated banks for which we have detailed income statement and balance sheet data (call reports and Y-9C ﬁlings). We estimate the

12 following regression:

CAP Mi,t − Rft = α + β1GLBt + β2Crisist + β3SCAPt + β4Dodd-F rankt

+ρBanki,t + δ1Banki,t · GLBt + δ2Banki,t · Crisist + δ3Banki,t · SCAPt (4) +δ4Banki,t · Dodd-F rankt + θ · Xi,t + φ1 · Xi,t · GLBt + φ2 · Xi,t · Crisist

+φ3 · Xi,t · SCAPt + φ4 · Xi,t · Dodd-F rankt + ei,t.

We continue to include the full panel of companies and add dummy variables for missing

regulatory data (omitted in the equation above). To proxy for capital and liquidity, we

include in X the proportion of total liabilities funded with core deposits, the Tier 1 capital

ratio, and a proxy for the liquidity coverage ratio (weighted assets divided by weighted

liabilities including oﬀ balance sheet commitments x 100)8. For asset composition and risk

we include the proportion of non-interest income to total income and the ratio of risk-

weighted assets to total assets. We also include speciﬁcations that decompose risk-weighted

assets into its components including the proportion of cash-equivalent assets, loans, trading

assets, commitments, and derivatives to total assets. All balance sheet items are measured

as of the most recent quarter. Table1 presents summary statistics for these variables in

Panel A over the full sample period. Panel B tabulates the value-weighted averages for each

regulatory regime, illustrating how the asset composition, funding mix and asset risk of the

banking industry have changed over time.

Changes in regulation can impact banks’ cost of capital by changing bank risk, capital,

liquidity, and business models. At the same time, bank managers may change their ﬁrm’s

characteristics in response to time-varying investment opportunities or in response to changes

in the market’s evaluation of bank risks, thereby impacting their cost of capital. We decom-

8LCR proxy uses regulatory data to approximate the LCR ratio as follows: Assets are weighted and include: Cash, FF Repo, US treasury, Agency Securities, Municipal securities, MBS, Other securities, Loans. Liabilities include respective weights times the following: FF Repo, Trading Liabilities, Commercial Paper, OBM, Subdebt, Deposits. Oﬀ balance sheet securities include respective weights times the following: Unused commitments, Financial Standby Letters, Securities underwritten, Securities lent.

13 pose this by ﬁrst studying the impact of controlling for bank characteristics unconditionally

(φ = 0). We then interact the bank characteristics with the time period dummy variables

to allow the coeﬃcients to change over time (φ 6= 0). This allows us to understand whether

changes to expected returns arise from changes to the market price of risk for diﬀerent char-

acteristics both within and across ﬁrms. For example, if liquidity has a large and signiﬁcant

coefficient only in the SCAP time period, this will be reflected in the φ3 coefficient, absorbing

variation that would have been reﬂected in the SCAP time period dummy in regression spec-

ification4. The Appendix extends this analysis to the difference-in-differences regressions

for the Top banks.

3.4 Eﬀect of stress testing

We also look in detail at the eﬀect of stress testing on the cost of capital by adopting the

identiﬁcation approach of Flannery et al.(2017) to estimate how stress tests impact the cost

of capital:

CAP Mi,t − Rft = α + β1GLBt + β2Crisist + β3SCAPt + β4P re-CCARt+

β5P ost-CCARt + β6SCAP F irmi + β7CCAR F irmi + β8SCAP F irmi · SCAPt (5) +β9SCAP F irmi · P re-CCARt + β10SCAP F irmi · P ost-CCARt

+β11CCAR F irmi · P ost-CCARt + θ · Xi,t + ei,t.

Each specification includes a set of non-overlapping time fixed effects and controls for bank

characteristics X. We split the banks into two groups based on the timing of their exposure

to Federal Reserve stress testing. The ﬁrst banks exposed to stress testing are captured

by the binary variable SCAP F irmi which is equal to 1 for the largest BHCs that were

initially included in stress tests beginning with SCAP in 2009.9 The next banks exposed

9Two US stress tested firms were not public for the entire sample. The first observation for Ally (SCAP) is April 2015 and the first observation for Citizens (CCAR) is September 2015.

14 to stress testing are captured by the binary variable CCAR F irmi which is equal to 1 for

the banks subjected to Comprehensive Capital Analysis and Review (CCAR) stress tests

starting in 2014 (“CCAR 2014 Addition”). The regulatory time periods are also changed to

accommodate the phased implementation of stress testing by splitting the DFA period into

two sub-periods before and after the expansion of ﬁrms subject to stress testing:

1. P re-CCARt: Passage of the Dodd-Frank Act when the 18 ﬁrms (SCAP F irmi) are

subject to stress testing and associated disclosure (July 2010 to August 2013)

2. P ost-CCARt: Addition of 7 ﬁrms (CCAR F irmi) to stress testing and associated

disclosure (September 2013 to December 2017)

As in Flannery et al.(2017), we limit the panel to the top 90 banks by assets each month to ensure that our comparison group of non-stress-tested banks is closer to the group of stress-tested banks.

3.5 Eﬀects on credit supply

We are interested in understanding if changes in the cost of capital for banks have effects on the real economy through the provision and pricing of credit. For this, we make use of the Senior Loan Officer Opinion Survey (SLOOS), which provides qualitative and limited quantitative information on the standards and terms of bank lending, business conditions, and household demand for loans as measured by survey responses of senior loan officers.

We make use of the SLOOS data because it oﬀers a way to separate changes to lending standards from changes in demand. This approach is superior to a simple estimation of the relationship between loan balances and interest margins using bank holding company data, because those measures conﬂate the supply of bank lending with demand.10 The Federal

10We do not estimate a statistically signiﬁcant relationship between quarterly changes in loan balances or interest margins and banks’ cost of capital.

15 Reserve conducts the SLOOS at a quarterly frequency covering questions about changes in the supply and demand for loans over the previous three months as well as special topics on evolving developments and lending practices in U.S. loan markets. As of 2017, the panel of reporting banks in the SLOOS included up to eighty large domestically chartered commercial banks that span all Federal Reserve Districts and up to 24 large U.S. branches and agencies of foreign banks that are primarily located in the New York District.

Our analysis focuses on questions that cover changes in lending standards and loan terms relative to the previous quarter. Using survey responses instead of measuring balance sheet loan growth or changes in interest income allows us to focus on the supply eﬀect at the individual bank level. We make use of survey questions on credit standards such as this example from the July 2018 SLOOS:

Over the past three months, how have your bank’s credit standards for approving appli-

cations for C&I loans or credit lines—other than those to be used to ﬁnance mergers

and acquisitions—to large and middle-market ﬁrms and to small ﬁrms changed?

Possible survey responses included: eased considerably, eased somewhat, remained basically unchanged, tightened somewhat, and tightened considerably. The questions are collected for loan standards to both large and middle-market ﬁrms (annual sales of $50 million or more) as well as small ﬁrms. Consistent with previous work using this data, we code these categorical responses as variables equal to -2, -1, 0, 1, and 2 in our regression analysis, with higher numbers indicating a tightening of credit standards or a tightening of the terms for loans that banks are willing to approve including the cost of credit lines, the spread of loan rates over bank’s cost of funds, the premium charged on riskier loans, loan covenants, collateralization requirements, and the maximum size of credit lines.

The regression speciﬁcation for this analysis is:

16 SLOOSi,t = α + η · ∆(CAP Mi,t − Rft) + ei,t. (6)

We regress bank-level SLOOS survey responses, a quarterly change, onto one-year changes in bank-level CAPM cost of capital estimates net of the risk-free rate. Similar results hold using six-month and two-year changes in the cost of capital and when we lag the change in the cost of capital by a quarter relative to the survey response. In addition, we also report specifications that control for one-year changes in the risk-free rate and one-year lagged realized bank-level stock market returns. This helps to confirm that we are identifying a relationship between the CAPM cost of capital and lending supply and that the results are not explained by omitted variables like bank distress. Finally, we add time fixed effects to absorb business cycle variation in the survey responses. A positive coefficient on η in these regressions indicates that bank managers are tightening credit standards or loan terms when their cost of capital is increasing.

4 The impact of regulation on the cost of capital

Over the last twenty years, value-weighted expected returns for banks averaged 11.5% based on an unbalanced panel of 1,447 banks. This compares to expected returns for non-banks of

10.0% (value weighted, based on an unbalanced panel of 10,545 non-banks). The risk-free rate averaged 2.2% over our sample period, and as mentioned in Section2, we set the level of the equity risk premium to 8% for our baseline cost of capital estimates. In comparison to these averages, Table2 presents the results from estimating equation2 on diﬀerent panels of ﬁrms. Dependent variables include the CAPM cost of capital and risk premium (CAPM and CAPM-Rf), the Fama and French(1993) three-factor risk premium (FF3-Rf), and the monthly realized excess return multiplied by twelve (Realized-Rf). Regressions are estimated

17 on an equal-weighted (EW) basis as well as a value-weighted (VW) basis.11 The average level of the estimated cost of capital in any time period can be calculated by summing the coeﬃcient for the time period with the constant, which captures the average (EW) or weighted average (VW) for the pre-GLB period.

4.1 Diﬀerence-in-diﬀerences across industries

In order to see if changes in the cost of capital for banks are different from those of non-banks over time, Table3 combines all firms into a single panel and estimates the specification in equation (3) for the CAPM cost of capital and risk premium. The decline of more than 4 percentage points in the risk free rate since the late 1990s is reflected in column (1).

In the remaining columns we explore differences between banks and nonbanks. We estimate that banks’ value-weighted cost of capital is about 70 basis points higher than that of other firms on average, consistent with the higher systematic risk of banks as evidenced by their average value-weighted beta of 1.17. But this premium has changed over time relative to the pre-GLB period. In the GLB period, the cost of capital for banks is unusually low relative to non-banks (Bank x GLB coefficient of -1.25). This result is surprising because most interpret GLB as being deregulatory and therefore related to an increase in the systemic risk of banks. In the Dodd-Frank period, the cost of capital for banks is 3% lower overall but

1.90% higher relative to non-banks (Dodd-Frank coefficient of -4.91 + Bank x Dodd-Frank coefficient of 1.90). Changes in banks’ cost of capital diverge the most from non-banks in the period immediately following the financial crisis and prior to the passage of the DFA – comparing the current period to the SCAP period, banks’ cost of capital fell by approximately 4.5% (Bank x SCAP coefficient of 6.55 minus Bank x Dodd-Frank coefficient of 1.90), while the change in the cost of capital in those time periods for non-banks was roughly zero

11The value weights are proportional to lagged market capitalization and are normalized each month by the total lagged market capitalization of all ﬁrms in the panel.

18 (SCAP coefficient of -5.02 minus Dodd-Frank coefficient of -4.91). This suggests that the net effect of Dodd-Frank was to reduce the systematic risk of banks, with reforms like increased capital and liquidity requirements more than offsetting opposing effects such as reductions in too-big-to-fail guarantees, and is consistent with post-financial crisis regulation moving the systematic risk of banks back towards the pre-deregulation period of the late 1990s.

These results are not driven by the addition of non-depository institutions such as investment banks and credit card companies to our definition of banks in 2009. In the third column we add firm fixed effect and find that the within firm cost of capital for banks differentially increases after the financial crisis and then falls by around 4.5%. At the same time, the within firm cost of capital for banks has returned to a level around 2.5% higher than that of non-banks relative to the pre-period. This could be consistent with an increase in the perceived riskiness of the industry due to a reduced probability of government assistance or with a re-evaluation of the systematic risk of the banking industry in general. Results are also robust to limiting the sample to banks and non-bank financial intermediaries, although the estimated coefficient on Bank x SCAP falls by almost half in this specification.

The difference between the Bank x SCAP coefficient of 3.69 and the Bank x Dodd-Frank coefficient of 1.42 is economically and statistically significant, indicating that banks’ cost of capital declined by about 2.25% relative to non-bank financials.

To the extent that different banks serve different borrowers, it is important to understand these changes not just on an industry level, but also on an equal-weighted basis to inform us about the change in the cost of capital for the average bank. In contrast to the value- weighted results, the change in banks’ cost of capital after the financial crisis is much smaller when the results are equal-weighted. In fact, in the cross section, the cost of capital is lower in the Dodd-Frank period relative to the pre-period for the average bank (specification 5).

However, looking within firm, the sign flips and we see a differential increase of around

19 1.75% relative to the pre-period (speciﬁcation 6). Overall these results are consistent with the decline in banks’ cost of capital post-crisis arising from changes to the cost of capital for the largest banks. We explore this question in more detail in the next section.

The last two columns repeat the analysis with a dependent variable equal to the CAPM cost of capital minus the risk-free rate (CAPM - Rf). Changes between column (3) and (7) reflect the unbalanced panel and the regulatory time period dummies that are more coarse than monthly time fixed effects. In order to ensure that our subsequent analysis is not capturing changes in the risk-free rate, the remainder of the paper studies estimates of the cost of capital less the risk-free rate as the dependent variable.

4.2 Top ﬁrms

Table4 examines differences in the cost of capital for the largest banks and non-banks over time relative to smaller firms. We begin by documenting the general patterns – while Top non-banks have about 1.5% lower expected returns than non-Top non-banks, Top banks have about 2% higher expected returns than non-Top banks (Top coefficient of -1.46 + Bank x

Top coefficient of 3.41). The remaining specifications include interactions between our size indicator and the time periods to understand how these differences play out as regulations change. Consistent with our initial concerns about measurement, we estimate the difference between the largest firms and other firms in column 2 and find that this difference has changed over time for non-banks as well. Since the GLB period, the extent to which the largest firms have a lower cost of capital than do smaller firms has increased for all companies by around 2% as indicated by the negative and statistically significant coefficients on the

Top x time period interaction terms.

Looking across the various specifications in Table4, we find a negative relationship or no statistically significant difference for the Top banks in the Dodd-Frank period as measured

20 by the Bank x Top x Dodd-Frank coefficient. This can be seen graphically in figure2 which plots the value-weighted difference in the cost of capital for banks versus non-banks and for Top banks versus Top non-banks relative to non-Top banks versus non-Top non- banks over time. The difference between the Bank x Top x Dodd-Frank and Bank x Top x

SCAP coefficients is consistently negative and statistically significant in most specifications, meaning that the current cost of capital for the very largest banks has fallen since DFA.

Perhaps the best identified test of the effect of changes in regulation since DFA comes in specification 4 in which we limit the panel to only banks and non-bank financials, and estimate within firm effects. In this specification, we estimate that the cost of capital for the very largest banks relative to all non-banks is differentially lower by 2.45% since pre-GLB.

The difference has fallen by 1.18% since the financial crisis, although this difference is not statistically significant.

4.3 Bank characteristics and the cost of capital

While any study of the cost of capital for banks must take into account changes in the cost of capital for non-banks, we can learn more about the impact of regulation by looking within the universe of regulated banks for which we have detailed data from regulatory reports, as laid out in equation (4). The sample includes 1,023 publicly traded banks with regulatory data. As before, we continue to employ the difference-in-differences strategy by including the full panel of companies and adding dummy variables if companies are missing regulatory data. Table5 reports the results. For brevity we omit the time period dummy variables and bank indicator coefficients in the reported results, although these variables are included in all the specifications.

The ﬁrst column (1) in Table5 replicates the seventh column (7) in Table3 to provide a reference point. We add to this baseline speciﬁcation controls for the share of revenue that

21 is non-interest income, the ratio of liabilities that are core deposits, a measure of liquidity coverage, the Tier 1 capital ratio, and the ratio of risk-weighted assets to total assets. Sum- mary statistics for these bank characteristics are presented in Panel A of Table1. The extent to which the bank industry has changed over time is shown in Panel B of Table1, where each column tabulates the value-weighted average within a time period. For example, in the post-DFA period, capital ratios are higher while risk-weighted assets and loans are a smaller share of total assets. Other ratios peaked in the crisis and pre-DFA time periods such as derivatives and non-interest income share. Some of these changes in the summary statistics are impacted by the changes in the panel composition, such as the addition of investment banks to the panel in 2009. The regressions, however, control for the changing panel by including bank fixed effects. In particular, the second column (2) of Table5 adds all of these bank characteristics to our value-weighted specification with bank fixed effects, allowing us to control for changes over time in these observable measures within banks.

On average, bank characteristics do little to explain the way in which banks’ cost of capital has changed with the passage of the DFA. When we add controls for observable characteristics, the estimated coeﬃcients on the bank x time interaction terms barely change comparing column (2) to column (1). For example, the decline in the cost of capital between the SCAP and Dodd-Frank periods continues to be around 4.5% and is highly statistically signiﬁcant. This suggests that the changes in the cost of capital that we observe are not correlated with changes in observable characteristics.

But what if the importance of bank characteristics is varying over time? We explore this possibility in columns (3) to (7) by allowing the relationship with the cost of capital to vary in the diﬀerent regulatory time periods for non-interest income, core deposits, liquidity coverage, and capital (as measured by the Tier 1 capital ratio). Each of these columns examines one characteristic in isolation by adding interaction terms with the regulatory

22 time periods so the coefficients can vary over time. The final specification (8) includes all of the characteristics and their time period interactions together to highlight how the estimated coefficients on the bank x time interactions change in comparison to column (1), although in column (8) we do not report the characteristic x time interaction coefficients as in column

(2) for readability.

Consistent with Calomiris and Nissim(2014), the results in columns (3) to (6) indicate that there has been some variation in the association between banks’ cost of capital and bank characteristics across the regulatory time periods, but accounting for this time variation does not reverse the general patterns in banks’ cost of capital after the ﬁnancial crisis, such as the decline after DFA. The results do change, however, after including risk-weighted assets

(RWA) in column (7). While there is no statistically significant relationship between RWA and expected returns for most of the regulatory time periods, RWA emerges as a key driver of banks’ cost of capital during the post-crisis SCAP period with a coefficient that is positive and highly significant. Moreover, when this interaction is included, the difference between the coefficients on the Bank x SCAP and Bank x Dodd-Frank indicators falls to almost nothing and is no longer significant. This result suggests that after the financial crisis, market expected returns for banks with higher RWA increased dramatically, and then fell again after the passage of the DFA. As shown in the final specification (8) which incldes all the interactions, RWA appears to be the key variable driving the change in the results.

The result for RWA appears to be driven by changes in the association between the cost of capital and loans. We run similar regressions using key components of RWA such as liquid assets (cash, fed funds, and securities), loans, trading assets, commitments, and derivatives (results are in Appendix Table A.4). While none of the RWA components by itself reverses the general patterns in banks’ cost of capital over time, the biggest changes in the characteristic coeﬃcients during the SCAP period occur for loans and loan commitments,

23 which both become signiﬁcant and positive. Within loans, the coeﬃcients on real estate loans increase the most in SCAP period (not shown). This is consistent with a market increase in expected returns for banks with more real estate loans and loan commitments in the SCAP period that was subsequently reversed.

The time-varying association with RWA does not fully explain the decline in the cost of capital for the largest banks (see Appendix Table A.5). Across speciﬁcations that include controls for time-varying bank characteristics, the cost of capital for the largest banks continues to decline by 3% to 4% after the SCAP period. Since the largest banks are differentially subject to increased regulation, these results are consistent with an increase in regulation leading to lower risk and lower expected returns in the Dodd-Frank period. To lend further weight to this interpretation, we extend the analysis by looking speciﬁcally at a single regulatory change in the next section.

4.4 Stress tests

While it is hard to attribute changes in the cost of capital to particular regulations because so many regulations were changed at the same time for the same set of ﬁrms, we attempt to take advantage of the staggered implementation of stress testing on banks with more than

$50 billion in assets to understand how a particular regulatory change, stress testing, may have aﬀected the cost of capital for stress-tested banks. Table6 presents the results of this analysis. Rather than using an indicator for banks, the panel includes only the 90 largest banks by assets each month that have regulatory data and then use separate indicators for the sets of banks that became subject to stress testing at diﬀerent times.12

12Note that not all ﬁrms that are stress tested are publicly traded – we exclude from the analysis the banks with foreign parents, and Ally and Citizens join the panel only after IPO. Because of its bankruptcy and subsequent reorganization, we exclude CIT from the panel entirely. If included, it would be the only bank in its category, since it was added to stress testing in 2016, and it would be in the comparison, non-stress tested group before that time. Similarly, we exclude Metlife from the panel entirely due to its subsequent debanking.

24 On average, the cost of capital increases for the large banks in this panel relative to the pre-period. The coefficients on the time periods are all positive and statistically significantly different from zero. Relative to the pre-period, the cost of capital is 7% higher after SCAP,

4% higher after the DFA is passed and prior to the initial disclosure of stress testing results in 2012, and 3.5% higher in the post stress testing CCAR period. Figure3 illustrates these results by plotting the equal-weighted cost of capital for the SCAP, CCAR, and other banks in the top 90 by asset size. The plot indicates that the largest increase in the cost of capital during the ﬁnancial crisis and subsequent decline post-DFA occurs for the SCAP

firms relative to the other large banks. Table6 formalizes these results. The last rows include SCAP firm x time period interactions that allow the coefficients for SCAP firms to differ from other large banks after 2009 and a CCAR firm x Post-CCAR coefficient that allows CCAR firms to differ in the post stress testing CCAR period (specifications 2-4, 6-8).

We ﬁnd that, while SCAP ﬁrm’s cost of capital increased by 2 percentage points during the

SCAP period, their cost of capital fell after DFA and then continued to decline by 150 basis points in the post stress testing CCAR period relative to other large banks (speciﬁcation

3). This within-ﬁrm decline of more than 3% since the SCAP period is signiﬁcant at the

1% level and robust to including bank characteristics as unconditional control variables as in Table5. Similar to prior results, we include all controls in the regression and only report the coeﬃcient on the Tier 1 Capital ratio for readability (speciﬁcation 4).

The results indicate that the largest reduction in the cost of capital occurs for the very largest stress-tested banks. This means that stress testing has differentially reduced systemic risk for the very largest firms. While we think that the staggered introduction of firms to stress testing contributes identifying power, we cannot distinguish this hypothesis from the alternative explanation that it reflects other regulations to which only these very largest firms are subject have also been implemented with timing similar to that of CCAR. Generally,

25 since the cost of capital estimates in our approach require time to estimate betas, we think it is diﬃcult to identify changes in time windows shorter than those captured in this analysis.

5 The cost of capital and lending supply and pricing

While the CAPM costs of capital estimates are interesting on their own as measures of the systematic risk of banks as captured in equity market prices, in this section we motivate our interest in CAPM by examining the real effects of the changes in the cost of capital. Since we are interested in documenting the co-movement of the cost of capital at individual banks with bank lending supply, rather than more general co-movements driven by the business cycle, we focus on a cost of capital measure that nets out the risk free rate. We find that lending standards and the cost of capital move together – Figure4 plots the the average change in credit standards for large and middle-market firms against the average one-year change in the CAPM risk premium less the risk-free rate for the banks in the SLOOS survey. In aggregate, these variables are positively correlated and the average response to the business cycle is procyclical, with banks tightening standards during recessions and easing standards during expansions. We make use of the confidential bank-level data to examine this result in the cross-section while controlling for changes over time through quarterly time fixed effects.

This approach increases power, controls for the business cycle, and identiﬁes a relationship between bank-level credit standards and changes in the cost of capital net of the risk-free rate.

5.1 Changes in lending standards and the cost of capital

Table7 reports the results of this analysis in Panel A which presents a set of regressions of quarterly changes in lending standards (Std) as measured by survey responses in the

26 SLOOS onto one-year changes in the cost of capital net of the risk-free rate, similar to the approach described in equation6. The first three columns examine the relationship for the largest borrowers, while the second three columns look at responses to questions about smaller borrowers. We estimate a positive and significant coefficient on the change in the cost of capital indicating that bank managers are tightening credit standards when their cost of capital net of the risk-free rate is increasing. To interpret the magnitude of the point estimate, an increase in a bank’s CAPM beta from 1 to 2 would increase the cost of capital risk premium by 8% which translates into a 8 x .024 = 0.19 higher survey response, about one-fifth the magnitude of an increase from one category of the response to another or about one-half the standard deviation of the dependent variable which equals .47. When a bank’s cost of capital increases, lending standards are tightened. The effect is larger for large borrowers, although the difference is not statistically significant in all specifications.

We want to be sure that we are not just capturing variation in the business cycle or the impact of idiosyncratic bank shocks. To account for this, we add one-year changes in the risk- free rate and one-year bank-level stock market returns as control variables (speciﬁcation 2).

Including bank-level stock market returns is a challenging test for omitted variable bias that allows us to capture the extent to which a negative shock from bad loans or poor profits may contribute to tighter lending standards. As expected, we estimate a negative and significant relationship between loan standards and both control variables. When interest rates decline or bank stock returns are low, lending standards are tighter. Adding these controls reduces the coefficient on the change in the CAPM cost of capital by half, but it does not reverse the result. An increase in the CAPM cost of capital remains significantly and positively associated with tighter loan standards. Interpreting the magnitude of the coefficients, a one- standard deviation change in the cost of capital, risk-free rate, and realized return results in a .03, .15, and .06 change in lending standards (specification 2). Bank managers appear to

27 tighten credit standards when the cost of capital risk premium (∆ CAPM - Rf) increases, even after controlling for changes in the risk-free rate and for ﬁrm-level stock market returns.

Finally, we illustrate that the results are robust to including quarterly fixed effects (specification 3), a more comprehensive control for any time-varying shock that would affect bank lending supply. These time fixed effects increase the explanatory power from 14% to

26%, indicating the importance of robust controls for changes in the business cycle variation including the aggregate tightening of spreads during the financial crisis. Despite this, the change in the cost of capital remains significant with a similar magnitude to the second specification. The results are largely similar although of slightly smaller magnitudes for smaller borrowers (specifications 4-6).

5.2 Changes in lending terms and the cost of capital

In panels B and C of Table7, we go beyond broad lending standards and look separately at the effect of changes in the cost of capital on different lending terms covered in the SLOOS questions such as: the cost of credit lines, the spread of loan rates over bank’s cost of funds, the premiums charged on riskier loans, loan covenants, collateralization requirements, and the maximum size of credit lines. Each of these terms is a dependent variable in the different columns of Panel B (larger borrowers) and C (small borrowers). Since we found that quarterly

fixed effects contribute substantial explanatory power, we include quarter fixed effects in all the specifications, similar to the third specification from Panel A. We find that increases in banks’ cost of capital are associated with tightening in the supply and pricing of credit through all of the lending terms measured, with greater statistical and economic significance for larger borrowers. The estimated relationship is generally positive but not significant for smaller borrowers.

The spread of loan rates over a bank’s cost of funds and the premiums charged on riskier

28 loans are perhaps the survey responses that most directly relate to the cost of capital. Indeed, we estimate the largest relationship between changes in the cost of capital and the response to these questions. When a bank’s CAPM beta increases from 1 to 2, senior loan officers report a 0.14 to 0.12 higher survey response on average for loan spreads and premiums on riskier loans, about one-fifth of one standard deviation of the survey response. In addition to these impacts on loan prices, we also find that banks decrease the maximum size of credit lines and tighten loan covenants when their cost of capital increases, thereby reducing credit supply. The results for collateral requirements are similar but not significant. These varied findings highlight the rich nature of the SLOOS data. Rather than being restricted to only study the quantity and pricing of loans through quarterly changes in loan balances or interest margins in call report data, the SLOOS allows us to investigate the provision of credit along multiple dimensions from the perspective of senior loan officers who are responsible for allocating credit in the economy. Building on the prior literature that has documented a negative relationship between the cost of capital and investment for non-financials, our results provide new evidence that banks act in a similar fashion, tightening the supply and pricing of credit in the economy when their CAPM cost of capital increases.

6 Alternative cost of capital estimates

In general, misspecification of expected returns that is associated with our regulatory time periods could bias our results. The advantage of multifactor models is to potentially better measure expected returns, thereby reducing any bias. To understand the robustness of the results for the CAPM cost of capital, Table8 repeats the key difference-in-differences specifications for banks and top banks for different cost of capital estimates including three- factor estimates following Fama and French(1993), five-factor estimates that incorporate

29 additional interest rate and term spread factors, one-factor estimates with a time-varying equity risk premium, log CAPM betas that difference out the equity risk premium, and asset betas from the Merton(1974) model. Across the various estimates we consistently find a significant decrease in the cost of capital for the largest banks since the passage of the

DFA. Figure5 summarizes these results by plotting the value-weighted alternative cost of capital estimates alongside our estimates of asset betas and market leverage for the banking sector. As before, while the plot may be affected by the changing composition of the panel, we control for this in the regressions with firm fixed effects and document significant within

ﬁrm changes over time.

6.1 Multifactor cost of capital estimates

The Fama and French(1993) three-factor model (FF3) delivers cost of capital estimates that account for the variation in expected returns for small versus big firms and for value versus growth firms. As before, we define the FF3 cost of capital as the sum of time-varying betas multiplied by constant factor risk premiums. We set the factor risk premiums equal to the average excess returns for the tradeable factors from 1926 to 2017 which are equal to

8%, 4.6%, and 2.5% in annualized units for the market, size, and value factors respectively.

The average beta or loading on these factors for banks over the last twenty years has been

1.17 (0.54), 0.85 (0.43), -0.11 (0.41) respectively versus 1.17 (0.55) for the CAPM on a value-weighted (equal-weighted) basis.

Columns (1) and (2) of Table8 repeat the value-weighted difference-in-differences regressions with firm fixed effects from Tables3 and4 for banks and top banks. Compared to the previous results, the FF3 model indicates that banks’ cost of capital diverged the most from non-banks in the period immediately preceding the financial crisis, when value factor betas were declining and banks were trading more like growth firms, rather than exhibiting

30 a decline in the period immediately following the crisis. Another difference is the Bank x Dodd-Frank coefficient, which indicates that banks have exhibited a 1% decline in their within-firm FF3 cost of capital (column 1) versus generally positive and significant estimates for the CAPM model. This fall in the cost of capital is driven by the largest banks, as shown in the results in column (2). For the top banks, the FF3 cost of capital has differentially fallen since the passage of the DFA by about 3%, similar to the CAPM regressions. More- over, the Bank x Top x Dodd-Frank coefficient is large in economic magnitude and highly significant, indicating that the FF3 cost of capital has differentially declined for the largest banks relative to the pre-GLB period as well. These results are stronger than the Top regressions for the CAPM which also feature negative coefficients on Bank x Top x Current but with magnitudes that are smaller and less significant. By capturing the changing loadings on the value and size factors during the financial crisis, the FF3 analysis indicates that the cost of capital for the largest banks has differentially fallen by as much as 3% relative to both the pre-GLB period and since the passage of the DFA.

In addition to size and value, other factors that affect expected stock returns for banks differently from other companies and that are correlated with the business cycle have the potential to bias our results. One such factor may be changes in interest rates, as maturity transformation and interest rate risk management are key aspects of bank business models, but may be less important for non-bank firms. To that end, we form a five-factor model (IR) that adds a short-term interest rate factor and a yield curve slope factor to the three-factor model. Columns (3) and (4) of Table8 report the results. To maintain consistency with our prior results, we use tradeable interest rate factors that are constructed from zero-coupon bond prices using the yield curve from Gurkaynak et al.(2006). 13 Having controlled for

13 1 The interest rate factors are Rshort,t = R2y,t − Rf,t and Rslope,t = 5 (R10y,t − Rf,t) − (R2y,t − Rf,t) where R2y,t and R10y,t are the daily return for two-year and ten-year zero coupon bonds and Rf,t is the daily risk-free rate. The slope factor has zero duration by construction and is -99% (-74%) correlated with the change in the 10y-2y zero-coupon (constant maturity) slope at a daily frequency. The short term factor is

31 interest rates in this manner, we confirm our CAPM cost of capital finding that banks exhibit a large and significant decrease in their cost of capital after the passage of the DFA relative to both the SCAP and pre-GLB periods. The decrease of approximately 4.5% relative to the pre-GLB period is large relative to both the CAPM and FF3 models (column 3). The Top regression confirms that the largest banks are driving this result, with a differential decline of 3% relative to the SCAP period and 5% relative to the pre-GLB period (column 4).

6.2 CAPM with a time-varying equity risk premium

A time-varying risk premium that is correlated with bank betas may bias our results. For example, if bank betas and the equity risk premium both increased in the Crisis and SCAP periods and then declined in the Dodd-Frank period, our estimate of the decline in the cost of capital for banks assuming a constant risk premium will be underestimated, all else equal.

To address this concern we consider two approaches. First, we use a model to estimate the equity risk premium and then repeat our analysis for the CAPM with this time-varying risk premium. To do this, we form a one-factor partial least squares estimate of the equity risk premium by combining 14 models of the equity risk premium from Duarte and Rosa

(2015) with available data from 1965 to 2016.14 We then project one-year ahead CRSP value-weighted returns onto the partial least squares estimate and use the ﬁtted value as a measure of the equity risk premium. This approach has the advantage that it directly addresses the concern that the equity risk premium is time varying but the disadvantage that the results are model and sample dependent.

For an alternative perspective, we take advantage of the fact that the equity risk premium

-99% (-94%) correlated with the change in the 2y zero-coupon (constant maturity) yield at a daily frequency. The average factor risk premiums from 1975 to 2017 are µshort = 1.14% and µslope = −.41% (the average annualized excess return for the 10-year zero coupon bond is 3.67%). 14Similar results hold by projecting one-year ahead returns onto the estimate of the equity risk premium from a dividend discount model, which is one of the 14 models included in the partial least squares estimate.

32 drops out of a diﬀerence-in-diﬀerences analysis after taking the logarithm since the CAPM

is a one-factor model.15 We thus estimate our diﬀerence-in-diﬀerences regressions using the logarithm of the CAPM betas as the dependent variable. We implement this idea empirically by winsorizing the estimated betas at .05 to remove negative values from the sample.

Table8 reports the baseline regressions for the CAPM using the partial least squares estimate of the equity risk premium (PLS-Rf) and for the logarithm of the CAPM betas

(Log(Beta)).16 For the PLS-Rf regressions almost all of the time period coefficients are larger than those in the specifications with a constant risk premium. This reflects the fact that our estimate of the time-varying equity risk premium has increased over the sample period, consistent with the findings in Duarte and Rosa(2015). For banks, the results are generally consistent with those from other CAPM specifications, in that the estimated cost of capital is higher in the Dodd-Frank period relative to the pre-GLB period but significantly lower than the SCAP period. Column (5) indicates that the cost of capital for banks has declined by around 9% from the SCAP period to the Dodd-Frank period. Column (6) shows that these results are again driven by the very largest banks. In comparison to the previous results, the larger magnitudes suggest that the assumption of a constant equity risk premium may be biasing our results down. Equivalently, the results suggest that bank betas are positively correlated with the equity risk premium.

Similar results also hold when taking the logarithm of the CAPM betas as the dependent variable in columns (7) and (8). For example, columns (7) and (8) indicate that bank CAPM betas have declined by about 35% from SCAP to Dodd-Frank with much of the decline being driven by the largest banks. One diﬀerence from the PLS-Rf results in column (6) is the

15 In particular, log(βi,tµt) − log(βi,t−1µt−1) − (log(βj,tµt) − log(βj,t−1µt−1)) = log(βi,t) − log(βi,t−1) − (log(βj,t) − log(βj,t−1)) . This argument does not apply to multifactor models. 16The PLS-Rf results are from March 1996 to 2016 when the equity risk premium estimates are available from Duarte and Rosa(2015). This results in a slightly smaller sample and contrasts the other regressions which end in 2017.

33 negative and signiﬁcant coeﬃcient on Bank x Top x Dodd-Frank in column (8). The negative

coeﬃcient for log betas is consistent with the CAPM, three-factor, and ﬁve-factor cost of

capital estimates using constant factor risk premiums which all indicate that the cost of

capital for the largest banks has declined relative to both the pre-GLB and SCAP periods

on a within ﬁrm, value-weighted basis.

6.3 Asset betas

The key component driving changes in our cost of capital estimates is the estimate of eq-

uity betas. In this way, the analysis captures changes to the systematic risk of the banking

industry. However, since these estimates are aﬀected by leverage we may also be interested

in looking directly at asset betas, which may better capture the systematic risk of banking

assets, regardless of capital structure changes. We compute asset betas in the Merton(1974)

model using equity market capitalization and equity volatility for each ﬁrm-month observa-

tion in the sample following the approach in Bharath and Shumway(2008). 17 This analysis

directly incorporates leverage into the estimated beta rather than including leverage as a

linear control variable in reduced form regressions as in Table4 (speciﬁcation 5) or in Table

5 (speciﬁcation 6) (where leverage is included as a time-varying characteristic as measured

by the Tier 1 capital ratio). The disadvantage of this approach is that the computation of

asset betas is model speciﬁc and requires a number of assumptions, such as how to compute

the maturity and face value of debt. These assumptions may be particularly important for

banks.

Columns (9) and (10) in Table8 report the results with asset beta as the dependent

17We compute asset betas by solving for ﬁrm value and volatility from two nonlinear equations for the simul value of equity and equity volatility, similar to how the default probability πMerton is computed in Bharath and Shumway(2008). To do this we assume that debt matures in one year and deﬁne the face value of debt as short-term debt plus one-half long-term debt plus deposits if available. In a previous draft we found similar results by assuming that debt was riskless as in Baker and Wurgler(2015) in which case asset betas asset are equal to βi,t = βi,t(1 − Li,t) where Li,t = Di,t/(Di,t + MEi,t).

34 variable. Looking at the bank interaction coefficients on the regulatory time periods, we still estimate a significant decrease in banks’ asset betas between the SCAP and Dodd-Frank periods that is primarily driven by the very largest banks. This result is noteworthy as the significant decline persists despite the decrease in bank leverage in recent years, which would imply increased asset betas of banks if equity betas were unchanged. From a longer historical perspective, bank asset betas have increased relative to the pre-GLB period by around .10 as measured by the significant and positive Bank x Top x Dodd-Frank coefficient in column

(10). This result diﬀers from the cost of capital estimates which generally feature a negative diﬀerence for the largest banks.

6.4 Weighted average cost of capital

In communications with investors and employees, bank managers reference ROE targets which are often compared the cost of equity capital. Pennacchi and Santos(2018) document that bank stocks appear to respond to ROE changes. However, given that banks are heavily

ﬁnanced with debt and deposits, an equity based measure may not capture the average (nor marginal) ﬁnancing cost for a bank.

Therefore, we repeat our analysis for the weighted average cost of capital (WACC), another commonly used measure of the cost of capital that takes into account the after-tax cost of debt, the cost of equity, and the capital structure. We estimate WACC from merged

CRSP-Compustat data as,

MEi,t Di,t W ACCi,t = Rei,t · + Rdi,t · (1 − τi,t) · , (7) Di,t + MEi,t Di,t + MEi,t

where Rei,t is the cost of equity capital as estimated in equation1, Rdi,t is the cost of debt, τi,t is the eﬀective tax rate, Di,t is total debt, MEi,t is market equity, and Li,t =

35 18 Di,t/(Di,t + MEi,t) is market leverage. When deﬁning total debt for banks, we add the total amount of deposits to capture this important component of bank leverage. The resulting leverage in the Dodd-Frank period is 0.81 for banks and 0.19 for non-banks (see Table1 for changes in leverage across periods). Note also that our cost of debt measure is based on accounting data so may adjust slowly over time. This diﬀers from our estimates of the cost of equity capital which are based on market prices, but is consistent with empirical evidence on sticky deposit pricing.

Table9 reports the difference-in-differences regressions using WACC-Rf as the dependent variable. The first column (1) indicates that value-weighted WACC-Rf has increased by about 1% over the past twenty years for all firms. The second column (2) indicates that bank WACC-Rf is almost 6% lower than non-bank WACC-Rf on average, reflecting the high leverage and low interest rates of banks relative to non-banks. Similar to the previous results, the second (2) and third (3) columns also indicate that WACC-Rf has fallen for banks between the SCAP and Dodd-Frank periods by around 1%, but increased between the Dodd-Frank and pre-GLB periods by around 1.5%. For the Top banks we see a further decrease in WACC-Rf by around 20 to 30 basis points in the specifications with firm fixed effects and the equal-weighted regression without fixed effects (specifications 5, 6, 7), but an increase in the value-weighted regression without fixed effects of around 15 basis points.

In contrast to the previous results, the changes for Top Banks are not signiﬁcant when comparing the SCAP and Dodd-Frank periods, although we still see a decline across most

18The cost of debt is a one-year moving average of quarterly interest expense over total debt which includes deposits. Total debt is long-term debt (Item DLTTQ) plus short-term debt (Item DLCQ) plus deposits if available (Item DPTCQ). Depending on availability, we use Item XINTQ or Item TIEQ in that order for quarterly interest expense. The effective tax rate is a one-year moving median of quarterly income taxes (Item TXTQ) over pre-tax income (Item PIQ). We winsorize the cost of debt, the effective tax rate, and market leverage at the 1% and 99% percentiles to mitigate the impact of outliers and measurement error. This data cleaning step is performed separately for financials and non-financials each month to allow for differences in firm characteristics and time trends, such as the high leverage of financial firms and the lower cost of debt and tax rates in recent years.

36 specifications. For the cost of equity capital we consistently found a large and significant decline across specifications when comparing the SCAP and Dodd-Frank periods.

7 Conclusion

Banks’ cost of capital is an input into decisions about lending quantities and pricing as well as decisions regarding resource allocation to different business lines. This paper rigorously estimates the cost of capital for the banking industry and explores how it has changed over time. After spiking in the financial crisis, the cost of capital for the banking industry has fallen dramatically since the passage of the Dodd-Frank Act. Expected returns for the very largest banks most affected by regulation have fallen differentially by 1% to 3% relative to post-financial crisis highs depending on the metric. Since these measures are driven by changes in equity and asset betas, this means that the systematic risk of these firms has fallen since the passage of the Dodd-Frank Act. For the largest banks in particular, there has been a differential decline relative to both the financial crisis and relative to the late

1990s across diﬀerent measures and regression speciﬁcations. This is striking in the face of research such as Atkeson et al.(2018) that suggests that the value of government guarantees are falling over the same period of time.

While these results suggest that the systematic risk of banks has declined in the post

Dodd-Frank era, it is worth noting the limitations of any analysis that seeks to understand the cost of capital. The true cost of capital measure relevant to bank managers is the unobserved expected returns of bank investors. Bank managers and econometricians do not have a time series of expected returns, only the models by which we estimate expected returns. Any test is thus a joint test of changes to expected returns and of the model for estimating expected returns. Some issues are alleviated by the diﬀerences-in-diﬀerences

37 approach. For example, the risk-free rate is added to the expected returns and thus drops out when differencing. Changes in banks’ cost of capital can be compared to other industries using different models, even if it is difficult to precisely estimate the level of banks’ cost of capital itself.

Ultimately, these questions are not just of academic interest. Our estimates of the cost of capital are capturing changes in market prices that matter to bank managers as reﬂected by changes in bank lending supply. The evidence suggests that the CAPM cost of capital for banks matters over and above changes in the risk free rates – increases in CAPM cost of capital are associated with tighter lending conditions, pricing, and quantity.

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41 Table 1: Summary Statistics for Cost of Capital Measures and Bank Variables Panel A reports summary statistics for banks and non-banks in the CRSP-Compustat universe from March 1996 to December 2017. CAPM is the expected return from a single factor market model. CAPM-Rf is the expected return in excess of the one-month Treasury bill rate. FF3-Rf is the excess expected return from the Fama and French(1993) three-factor model. WACC-Rf is the excess weighted average cost of capital. Realized-Rf is the monthly excess realized return multiplied by 12. Bank regulatory variables are obtained from call reports and Y-9C ﬁlings. Panel B reports weighted averages over diﬀerent time periods. The cost of capital is in annualized percentage units. Leverage is the ratio of total debt to total debt plus market equity, where we add deposits to total debt for banks.

Panel A Variable p25 p50 p75 mean sd count Nonbanks: CAPM 6.5 9.2 12.4 9.7 4.9 968938 CAPM - Rf 3.6 6.8 10.2 7.2 4.9 968938 FF3 - Rf 5.2 9.5 14.3 10.1 8.2 968938 WACC-Rf 2.8 5.3 7.9 5.6 3.8 521126 Realized - Rf -85.4 2.2 92.4 16.7 228.8 968938 Banks: CAPM 3.3 6.3 9.5 6.8 4.5 142189 CAPM - Rf 0.8 2.9 7.6 4.4 4.5 142189 FF3 - Rf 1.9 6.5 12.1 7.3 6.8 142189 WACC-Rf -1.1 0.5 1.3 0.2 1.8 128562 Realized - Rf -40.4 6.2 58.0 11.5 121.0 142189 Leverage 0.83 0.87 0.91 0.86 0.09 135921 Noninterest Income/ Total Income 14.2 21.1 29.8 60.7 3382.8 101457 Core Deposits / Total Liab. 52.0 60.3 68.2 58.9 14.1 101457 Liquidity Coverage Ratio 58.1 65.7 71.7 63.6 15.8 101457 Tier 1 Capital Ratio 10.5 12.1 14.4 13.2 6.5 99049 RWA / Total Assets 65.0 72.8 80.1 72.2 12.3 99049 Cash + FF Repo + Sec. / Total Assets 18.7 25.6 33.7 27.4 12.3 101457 Loan / Total Assets 60.3 68.2 75.0 66.2 13.7 101457 Trading Assets / Total Assets 0.0 0.0 0.0 0.5 2.9 101457 Commitments / Total Assets 10.5 15.4 22.2 19.9 37.2 101457 Derivatives / Total Assets 0.0 0.0 0.0 0.4 3.2 101457 Panel B Time Period Basel 1 GLB Crisis SCAP Dodd- Frank Noninterest Income/ Total Income 41.4 48.3 97.2 52.7 49.6 Core Deposits / Total Liab. 41.1 36.4 34.7 33.8 40.8 Liquidity Coverage Ratio 34.8 32.0 33.7 47.9 57.4 Tier 1 Capital Ratio 9.5 10.6 10.9 13.4 13.8 RWA / Total Assets 79.2 74.4 72.3 67.4 66.7 Cash + FF Repo + Sec. / Total Assets 26.7 28.7 26.9 33.1 34.4 Loan / Total Assets 60.6 52.7 51.2 42.8 46.7 Trading Assets / Total Assets 5.7 7.7 9.4 11.5 8.8 Commitments / Total Assets 70.8 71.7 55.3 45.4 46.0 Derivatives / Total Assets 4.2 7.5 11.6 16.8 12.5 Leverage - Banks and Nonbanks 0.25 0.26 0.26 0.28 0.25 Leverage - Banks 0.80 0.77 0.81 0.85 0.81 Leverage - Nonbanks 0.19 0.19 0.20 0.21 0.19

42 Table 2: The Cost of Capital for Banks and Non-Banks Over Time This table reports regressions of cost of capital measures onto a constant and time period dummies for banks and non-banks from March 1996 through December 2017. The dependent variables include the CAPM expected return, CAPM-Rf and FF3-Rf excess expected returns, WACC-Rf excess return, and realized excess return in annualized percent. Standard errors are clustered by ﬁrm and month with ∗, ∗∗, ∗∗∗ indicating signiﬁcance at the 10%, 5%, and 1% levels respectively. Cost of Capital Measure Constant GLB Crisis SCAP Dodd- N Frank

Banks, Equal Weighted

CAPM 7.91*** -1.58*** -0.09 -1.42*** -1.69*** 142189 (0.12) (0.27) (0.39) (0.31) (0.24) CAPM-Rf 3.04*** 0.24 2.33*** 3.33*** 2.99*** 142189 (0.15) (0.21) (0.25) (0.33) (0.24) FF3-Rf 8.89*** -3.75*** -0.24 -1.01** -0.19 142189 (0.33) (0.34) (0.53) (0.48) (0.42) Realized-Rf 16.91** -1.33 -47.16*** -4.66 1.80 142189 (7.69) (8.46) (15.96) (19.66) (9.14) Banks, Value Weighted

CAPM 13.59*** -3.15*** -0.60* 1.54* -3.01*** 142189 (0.33) (0.40) (0.36) (0.82) (0.40) CAPM-Rf 8.71*** -1.14*** 1.61*** 6.28*** 1.64*** 142189 (0.34) (0.38) (0.52) (0.83) (0.39) FF3-Rf 15.91*** -6.64*** -0.55 -0.25 -1.29* 142189 (0.44) (0.53) (0.81) (0.84) (0.69) Realized-Rf 19.17 -12.96 -60.64** -3.01 -4.95 142189 (11.96) (13.13) (24.30) (23.95) (13.76) Non-banks, Equal Weighted

CAPM 10.24*** -0.35 0.02 -1.44*** -1.25*** 968938 (0.12) (0.25) (0.44) (0.18) (0.16) CAPM-Rf 5.37*** 1.37*** 2.38*** 3.29*** 3.41*** 968938 (0.13) (0.21) (0.18) (0.19) (0.15) FF3-Rf 11.28*** -1.38*** -2.38*** -1.08*** -1.57*** 968938 (0.19) (0.23) (0.23) (0.22) (0.20) Realized-Rf 12.20 10.50 -24.18 31.67 6.08 968938 (10.46) (13.86) (20.42) (22.66) (11.93) Non-banks, Value Weighted

CAPM 12.93*** -1.90*** -2.74*** -5.02*** -4.91*** 968938 (0.18) (0.29) (0.44) (0.25) (0.22) CAPM-Rf 8.06*** -0.12 -0.26 -0.28 -0.26 968938 (0.17) (0.20) (0.23) (0.25) (0.22) FF3-Rf 6.97*** 0.84** 0.25 0.76 0.42 968938 (0.50) (0.35) (0.43) (0.47) (0.48) Realized-Rf 16.82** -15.86 -31.50** 1.82 -1.17 968938 (8.20) (10.08) (15.56) (16.42) (9.20)

43 Table 3: The Cost of Capital for Banks Compared to Other Industries This table reports the differential cost of capital for banks over time relative to other industries by regressing the CAPM expected return in annualized percentage units onto a constant and time period dummies along with indicator and interaction terms for banks. Regressions are value-weighted by market capitalization or equal-weighted with some specifications including firm fixed effects. Specification (4) is restricted to banks and non-bank financials where financials are defined as firms with two-digit SIC codes between 60 and 69. The sample includes monthly observations for 11,959 companies in CRSP-Compustat from March 1996 to December 2017. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels respectively.

(1) (2) (3) (4) (5) (6) (7) (8) CAPM CAPM CAPM CAPM CAPM CAPM CAPM - Rf CAPM - Rf GLB -2.03∗∗∗ -1.90∗∗∗ -2.54∗∗∗ -3.55∗∗∗ -0.35 -0.75∗∗∗ -0.83∗∗∗ 0.74∗∗∗ (0.27) (0.29) (0.27) (0.52) (0.25) (0.23) (0.20) (0.20) Crisis -2.55∗∗∗ -2.74∗∗∗ -3.23∗∗∗ -1.57∗∗∗ 0.02 -0.66 -0.85∗∗∗ 1.44∗∗∗ (0.41) (0.44) (0.44) (0.44) (0.44) (0.45) (0.25) (0.19) SCAP -4.38∗∗∗ -5.02∗∗∗ -5.44∗∗∗ -2.28∗∗∗ -1.44∗∗∗ -2.21∗∗∗ -0.82∗∗∗ 2.23∗∗∗ (0.30) (0.25) (0.30) (0.74) (0.18) (0.20) (0.29) (0.20) Dodd-Frank -4.75∗∗∗ -4.91∗∗∗ -5.54∗∗∗ -4.51∗∗∗ -1.25∗∗∗ -2.20∗∗∗ -0.98∗∗∗ 2.20∗∗∗

44 (0.21) (0.22) (0.26) (0.47) (0.16) (0.17) (0.25) (0.16) Bank 0.66∗ -3.26∗∗∗ -3.31∗∗∗ -2.33∗∗∗ -2.54∗∗∗ -3.15∗∗∗ -2.34∗∗∗ (0.37) (0.47) (0.53) (0.18) (0.53) (0.46) (0.54) Bank x GLB -1.25∗∗∗ -0.78∗ 0.23 -1.24∗∗∗ 0.22 -0.58 0.33 (0.45) (0.41) (0.60) (0.21) (0.23) (0.40) (0.24) Bank x Crisis 2.14∗∗∗ 2.50∗∗∗ 0.84 -0.11 1.97∗∗∗ 2.24∗∗∗ 2.05∗∗∗ (0.60) (0.65) (0.59) (0.30) (0.33) (0.65) (0.33) Bank x SCAP 6.55∗∗∗ 6.87∗∗∗ 3.69∗∗∗ 0.02 2.32∗∗∗ 6.88∗∗∗ 2.36∗∗∗ (0.88) (0.96) (1.05) (0.33) (0.34) (0.95) (0.34) Bank x Dodd-Frank 1.90∗∗∗ 2.46∗∗∗ 1.42∗∗ -0.44∗ 1.73∗∗∗ 2.45∗∗∗ 1.76∗∗∗ (0.46) (0.55) (0.65) (0.25) (0.27) (0.53) (0.27) Observations 1111127 1111127 1111062 223432 1111127 1111062 1111062 1111062 Adjusted R2 0.170 0.199 0.598 0.566 0.053 0.484 0.542 0.537 Fixed Effects No No Yes Yes No Yes Yes Yes Weighting VW VW VW VW EW EW VW EW Sample All Firms All Firms All Firms Banks+NBF All Firms All Firms All Firms All Firms Table 4: The Cost of Capital for the Largest Banks This table reports the differential cost of capital for the largest banks over time relative to large firms in other industries by interacting the binary variable T op with the time period dummies, the Bank indicator, and the Bank and time period interaction terms. T op is a binary variable equal to one when a firm is among the 20 largest firms as measured by assets within its Fama-French 12 industry. Regressions are either value-weighted by market capitalization or equal-weighted with some specifications including firm fixed effects. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf GLB -0.24 1.49∗∗∗ 0.60∗∗∗ -0.27 0.73∗∗∗ 1.43∗∗∗ 0.81∗∗∗ (0.19) (0.23) (0.19) (0.27) (0.17) (0.21) (0.21) Crisis -0.10 0.94∗∗∗ 0.24 1.15∗∗∗ 0.76∗∗∗ 2.43∗∗∗ 1.49∗∗∗ (0.21) (0.26) (0.26) (0.43) (0.22) (0.19) (0.21) SCAP 0.34 1.25∗∗∗ 0.50∗ 2.03∗∗∗ 1.36∗∗∗ 3.34∗∗∗ 2.25∗∗∗ (0.29) (0.26) (0.27) (0.53) (0.23) (0.20) (0.21) Dodd-Frank -0.10 1.22∗∗∗ 0.39∗ 0.69∗∗ 0.97∗∗∗ 3.53∗∗∗ 2.31∗∗∗ (0.21) (0.22) (0.23) (0.35) (0.21) (0.16) (0.17) Bank -0.91∗∗∗ -1.20∗∗∗ -3.00∗∗∗ -3.28∗∗∗ -2.46∗∗∗ -2.50∗∗∗ -1.88∗∗∗ (0.28) (0.40) (0.54) (0.55) (0.62) (0.17) (0.56) Top -1.46∗∗∗ 0.46 1.25∗∗∗ 1.05 1.70∗∗∗ 1.71∗∗∗ 1.10∗∗∗ (0.22) (0.31) (0.43) (0.65) (0.42) (0.19) (0.26) Bank x Top 3.41∗∗∗ 3.17∗∗∗ 0.13 0.25 -0.46 5.19∗∗∗ 0.37 (0.40) (0.53) (0.60) (0.73) (0.59) (0.30) (0.54) Bank x GLB -0.95∗ -0.03 0.87∗∗ -0.22 -1.08∗∗∗ 0.41∗ (0.50) (0.36) (0.38) (0.33) (0.22) (0.24) Bank x Crisis 1.85∗∗∗ 3.02∗∗∗ 2.15∗∗∗ 2.61∗∗∗ -0.08 2.10∗∗∗ (0.65) (0.53) (0.56) (0.50) (0.30) (0.34) Bank x SCAP 3.02∗∗∗ 4.42∗∗∗ 2.94∗∗∗ 3.91∗∗∗ -0.16 2.30∗∗∗ (0.65) (0.64) (0.75) (0.57) (0.32) (0.34) Bank x Dodd-Frank 1.69∗∗∗ 3.25∗∗∗ 3.02∗∗∗ 2.71∗∗∗ -0.52∗∗ 1.82∗∗∗ (0.46) (0.39) (0.44) (0.39) (0.25) (0.27) Top x GLB -2.50∗∗∗ -2.12∗∗∗ -2.71∗∗∗ -2.30∗∗∗ -1.46∗∗∗ -1.17∗∗∗ (0.41) (0.34) (0.70) (0.33) (0.26) (0.25) Top x Crisis -1.86∗∗∗ -1.57∗∗∗ -0.73 -1.91∗∗∗ -1.35∗∗∗ -0.84∗∗∗ (0.42) (0.41) (0.70) (0.40) (0.29) (0.31) Top x SCAP -2.34∗∗∗ -1.90∗∗∗ 2.07 -2.59∗∗∗ -1.23∗∗∗ -0.49 (0.42) (0.44) (1.36) (0.43) (0.36) (0.35) Top x Dodd-Frank -2.28∗∗∗ -1.94∗∗∗ -0.84 -2.35∗∗∗ -2.26∗∗∗ -1.48∗∗∗ (0.36) (0.37) (0.76) (0.37) (0.26) (0.28) Bank x Top x GLB -0.48 -0.99∗ -0.40 -0.66 -1.27∗∗∗ -2.32∗∗∗ (0.71) (0.55) (0.84) (0.54) (0.38) (0.39) Bank x Top x Crisis -0.50 -1.27∗ -2.13∗∗ -0.75 0.65 -0.88 (0.78) (0.70) (0.85) (0.61) (0.59) (0.62) Bank x Top x SCAP 3.81∗∗∗ 2.78∗∗∗ -1.27 3.26∗∗∗ 4.21∗∗∗ 2.04∗∗ (1.01) (1.07) (1.64) (1.02) (0.85) (0.87) Bank x Top x Dodd-Frank -0.23 -1.24∗ -2.45∗∗ -0.78 0.25 -1.86∗∗∗ (0.66) (0.63) (0.95) (0.66) (0.50) (0.52) Leverage 0.03 (0.58) Observations 1111127 1111127 1111062 223432 890583 1111127 1111062 Adjusted R2 0.055 0.092 0.551 0.599 0.561 0.111 0.538 Fixed Eﬀects No No Yes Yes Yes No Yes Weighting VW VW VW VW VW EW EW Sample All Firms All Firms All Firms Banks+NBF All Firms All Firms All Firms

45 Table 5: The Cost of Capital for Banks Controlling for Bank Characteristics This table reports the differential cost of capital for banks over time relative to other industries controlling for bank characteristics. Regulatory variables are obtained from call reports and Y-9C filings. The results are reported for expected excess returns in the CAPM in value-weighted regressions with firm fixed effects. The time period dummies and bank indicator are included in the regressions but omitted in the results for brevity. Column (1) replicates column (8) from Table3. Column (2) includes all of the characteristics unconditionally. Columns (3) to (7) allow the coefficients on each characteristic to vary over time through interaction terms. Column (8) includes all of the characteristics together with time-varying coefficients. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) (8) None All Non Int. Inc. Core Deposits Liq. Coverage Tier 1 RWA All Bank x GLB -0.58 -0.60 0.45 -1.82∗∗∗ -1.05∗∗ -1.07∗∗ 0.12 -0.20 (0.40) (0.37) (0.57) (0.53) (0.47) (0.46) (0.59) (0.51) Bank x Crisis 2.24∗∗∗ 2.24∗∗∗ 4.04∗∗∗ 0.36 0.95 1.74∗∗ 2.29∗∗∗ 2.34∗∗∗ (0.65) (0.62) (0.79) (0.77) (0.80) (0.71) (0.83) (0.78) Bank x SCAP 6.88∗∗∗ 6.76∗∗∗ 7.80∗∗∗ 3.49∗∗∗ 4.93∗∗∗ 6.87∗∗∗ 1.65 1.74 (0.95) (0.95) (1.22) (1.07) (1.50) (1.11) (1.49) (1.27) 46 Bank x Dodd-Frank 2.45∗∗∗ 2.31∗∗∗ 4.39∗∗∗ 0.27 0.81 2.03∗∗∗ 1.89 1.36 (0.53) (0.49) (0.66) (0.74) (0.95) (0.65) (1.28) (1.23) Characteristic 0.05∗∗∗ -0.07∗∗∗ -0.01 -0.01 0.01 (0.01) (0.02) (0.02) (0.03) (0.01) Characteristic x GLB -0.03∗∗ 0.03∗∗∗ 0.02∗ 0.05∗ -0.01 (0.01) (0.01) (0.01) (0.03) (0.01) Characteristic x Crisis -0.05∗∗∗ 0.05∗∗∗ 0.04∗∗∗ 0.05∗ -0.00 (0.01) (0.01) (0.01) (0.03) (0.01) Characteristic x SCAP -0.03 0.10∗∗∗ 0.05∗ 0.00 0.08∗∗∗ (0.02) (0.02) (0.03) (0.03) (0.02) Characteristic x Dodd-Frank -0.05∗∗∗ 0.06∗∗∗ 0.03∗ 0.03 0.01 (0.01) (0.01) (0.02) (0.03) (0.02) Observations 1111062 1111062 1111062 1111062 1111062 1111062 1111062 1111062 Adjusted R2 0.542 0.543 0.542 0.543 0.543 0.542 0.543 0.546 Fixed Effects Yes Yes Yes Yes Yes Yes Yes Yes Weighting VW VW VW VW VW VW VW VW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms Characteristic None All Non Int. Inc. Core Deposits Liq. Coverage Tier 1 RWA All Time Varying NA No Yes Yes Yes Yes Yes Yes Table 6: The Impact of Stress Testing This table reports the cost of capital for the largest 90 banks each month by assets with regulatory data from March 1996 to December 2017. The sample includes 227 banks in total and separates the Dodd-Frank period into Dodd-Frank: Pre-CCAR from July 2010 through August 2013 and Dodd-Frank: Post-CCAR from September 2013 through December 2017. SCAP Firm is a binary variable equal to 1 for banks included in the initial round of stress testing. CCAR Firm is a binary variable equal to 1 for banks that were later added to stress testing. Results are reported for expected excess returns in the CAPM and FF3 models. Regressions are equal-weighted with some specifications including firm fixed effects and control variables for bank characteristics. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) (8) CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf FF3 - Rf FF3 - Rf FF3 - Rf FF3 - Rf GLB 0.46 0.46 0.19 0.19 -4.86∗∗∗ -4.85∗∗∗ -4.80∗∗∗ -4.81∗∗∗ (0.30) (0.30) (0.28) (0.29) (0.40) (0.40) (0.43) (0.45) Crisis 4.20∗∗∗ 4.19∗∗∗ 3.84∗∗∗ 3.84∗∗∗ 3.26∗∗∗ 3.26∗∗∗ 3.45∗∗∗ 3.46∗∗∗ (0.44) (0.43) (0.48) (0.48) (0.98) (0.98) (1.01) (1.01) SCAP 6.96∗∗∗ 6.57∗∗∗ 6.40∗∗∗ 6.38∗∗∗ 1.68∗∗ 1.46∗ 1.86∗∗ 1.94∗∗ (0.61) (0.61) (0.62) (0.61) (0.73) (0.76) (0.81) (0.78) Dodd-Frank: Pre-CCAR 3.89∗∗∗ 3.92∗∗∗ 3.99∗∗∗ 4.01∗∗∗ 0.40 0.06 1.00 1.12∗

47 (0.33) (0.35) (0.40) (0.40) (0.54) (0.56) (0.66) (0.65) Dodd-Frank: Post-CCAR 3.46∗∗∗ 3.67∗∗∗ 3.88∗∗∗ 3.48∗∗∗ 1.04∗∗ 1.27∗∗ 2.76∗∗∗ 2.56∗∗∗ (0.40) (0.43) (0.47) (0.43) (0.50) (0.54) (0.63) (0.61) SCAP Firm 1.07∗∗∗ 1.24∗∗∗ -0.04 -0.15 (0.30) (0.36) (0.42) (0.45) CCAR Firm 0.23 0.23 -0.44 -0.43 (0.42) (0.45) (0.59) (0.53) SCAP Firm x SCAP 2.00∗∗∗ 1.95∗∗∗ 1.78∗∗ 1.20 1.11 1.00 (0.72) (0.75) (0.74) (0.90) (0.96) (0.98) SCAP Firm x DF: Pre-CCAR -0.20 -0.49 -0.62 1.76∗ 1.14 1.08 (0.54) (0.55) (0.57) (0.90) (0.88) (0.90) SCAP Firm x DF: Post-CCAR -1.10∗∗ -1.50∗∗∗ -1.55∗∗∗ -1.10 -2.25∗∗∗ -2.19∗∗∗ (0.44) (0.48) (0.49) (0.73) (0.74) (0.78) CCAR Firm x DF: Post-CCAR -0.06 -0.51 -0.59 -0.06 -0.94 -1.04 (0.40) (0.40) (0.43) (0.75) (0.70) (0.73) Tier 1 Capital Ratio -0.01 -0.02 (0.02) (0.03) Observations 23347 23347 23347 23347 23347 23347 23347 23347 Adjusted R2 0.364 0.369 0.581 0.592 0.319 0.323 0.506 0.509 Fixed Effects No No Yes Yes No No Yes Yes Controls No No No Yes No No No Yes Weighting EW EW EW EW EW EW EW EW Table 7: The CAPM Cost of Capital and Lending Supply This table reports regressions of quarterly changes in lending standards as measured by survey responses onto one-year changes in the CAPM risk premium (∆ CAPM - Rf) from March 1996 to December 2017. Panel A regresses the change in lending standards (Std) onto different specifications that include one-year changes in the risk-free rate (∆ Rf) and one-year realized bank-level stock market returns (Realized Return) and quarter fixed effects. Panels B and C regress changes in the terms for loans that banks are willing to approve to large and middle-market firms (LM) and small firms (S) onto one-year changes in the CAPM risk premium with quarter fixed effects. The loan terms include the cost of credit lines (CCL), the spread of loan rates over bank’s cost of funds (Spd), the premiums charged on riskier loans (RP), loan covenants (Cov), collateralization requirements (Col), and the maximum size of credit lines (Max). The positive and significant coefficients across specifications and loan terms in Panels A and B are consistent with the interpretation that bank managers tighten credit standards and charge wider spreads for large and middle-market firms when their cost of capital increases.

Panel A: ∆ Lending Standards Std-LM Std-LM Std-LM Std-S Std-S Std-S ∆ CAPM - Rf 0.024*** 0.012*** 0.011** 0.021*** 0.010** 0.007* (0.007) (0.004) (0.005) (0.007) (0.004) (0.004) ∆ Rf -0.131*** -0.114*** (0.020) (0.018)

48 Realized Return -0.002*** -0.002*** (0.001) (0.001) Observations 3776 3776 3776 3672 3672 3672 Adjusted R-squared 0.019 0.159 0.262 0.018 0.153 0.241 Quarter Fixed Eﬀects No No Yes No No Yes Weighting EW EW EW EW EW EW

Panel B: ∆ Loan terms for large and middle-market firms, equal weighted, quarter fixed effects CCL Spd RP Cov Col Max ∆ CAPM - Rf 0.015** 0.018*** 0.016** 0.012** 0.006 0.008* (0.007) (0.007) (0.006) (0.005) (0.004) (0.005) Observations 3760 3760 3462 3761 3757 3759 Adjusted R-squared 0.304 0.366 0.313 0.209 0.185 0.180

Panel C: ∆ Loan terms for small firms, equal weighted, quarter fixed effects CCL Spd RP Cov Col Max ∆ CAPM - Rf 0.006 0.005 0.008 0.006 0.004 0.004 (0.006) (0.006) (0.006) (0.004) (0.004) (0.005) Observations 3639 3639 3351 3639 3634 3636 Adjusted R-squared 0.256 0.318 0.267 0.171 0.157 0.138 Table 8: Alternate Cost of Capital Estimates for Banks This table reports the differential cost of capital net of the risk-free rate for banks and for the largest banks as measured by the Fama and French(1993) three-factor model (FF3-Rf) in columns (1) to (3), a five-factor model that combines the Fama and French(1993) factors with tradeable interest rate factors for the short rate and slope of the yield curve (IR-Rf) in columns (4) to (6), and the weighted average cost of capital (WACC-Rf) in columns (7) to (9). Regressions are value-weighted by market capitalization with some specifications including firm fixed effects. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) FF3 - Rf FF3 - Rf IR-Rf IR-Rf PLS-Rf PLS-Rf Log(Beta) Log(Beta) Asset Beta Asset Beta GLB 1.33∗∗∗ 0.78∗∗ 1.14∗∗∗ 0.58 5.13∗∗∗ 5.04∗∗∗ -0.21∗∗∗ 0.05 -0.11∗∗∗ 0.06∗∗∗ (0.43) (0.37) (0.41) (0.39) (0.63) (0.70) (0.04) (0.03) (0.03) (0.02) Crisis 0.58 -0.62 0.54 -0.62 9.08∗∗∗ 9.10∗∗∗ -0.08∗∗ 0.11∗∗∗ -0.11∗∗∗ 0.04 (0.49) (0.41) (0.49) (0.43) (0.71) (0.69) (0.04) (0.03) (0.03) (0.03) SCAP 1.39∗∗ 0.55 1.36∗∗ 0.48 14.77∗∗∗ 16.19∗∗∗ -0.10∗∗ 0.13∗∗∗ -0.13∗∗∗ 0.07∗∗∗ (0.55) (0.40) (0.55) (0.43) (0.64) (0.57) (0.04) (0.03) (0.03) (0.03) Dodd-Frank 1.02∗ -0.34 1.23∗∗ 0.01 13.12∗∗∗ 14.36∗∗∗ -0.10∗∗∗ 0.14∗∗∗ -0.13∗∗∗ 0.05∗∗ (0.54) (0.40) (0.54) (0.43) (0.46) (0.44) (0.04) (0.03) (0.03) (0.03) Bank 0.91 -0.58 2.16 0.45 -1.06 1.32 -0.41∗∗∗ -0.36∗∗∗ -0.08∗ 0.03 (1.32) (1.20) (1.36) (1.31) (1.34) (1.46) (0.07) (0.07) (0.04) (0.05) Bank x GLB -7.70∗∗∗ -5.00∗∗∗ -6.59∗∗∗ -3.55∗∗∗ 1.38∗∗∗ 0.62 0.07 0.10∗ 0.04 -0.08∗∗∗ (0.65) (0.53) (0.66) (0.59) (0.32) (0.39) (0.06) (0.06) (0.03) (0.02) Bank x Crisis -0.52 2.03∗∗ -0.51 2.84∗∗∗ 4.02∗∗∗ 2.03∗∗∗ 0.27∗∗∗ 0.44∗∗∗ 0.06 -0.00 49 (0.98) (0.93) (0.94) (0.90) (0.73) (0.60) (0.08) (0.07) (0.04) (0.04) Bank x SCAP -0.60 -0.37 -0.81 0.28 14.02∗∗∗ 4.59∗∗∗ 0.66∗∗∗ 0.60∗∗∗ 0.18∗∗∗ -0.02 (1.09) (0.80) (1.15) (0.98) (1.82) (0.88) (0.09) (0.08) (0.05) (0.04) Bank x Dodd-Frank -1.17 1.41∗∗ -4.48∗∗∗ -1.07 5.34∗∗∗ 1.29∗∗ 0.32∗∗∗ 0.50∗∗∗ 0.04 -0.04 (0.99) (0.67) (1.06) (0.71) (0.89) (0.51) (0.07) (0.06) (0.04) (0.03) Top -1.47∗ -1.57∗∗ 1.51∗∗∗ 0.27∗∗∗ 0.16∗∗∗ (0.78) (0.76) (0.50) (0.06) (0.05) Bank x Top 2.53∗∗ 2.97∗∗∗ -3.78∗∗∗ -0.01 -0.14∗∗∗ (1.07) (1.14) (1.09) (0.08) (0.05) Top x GLB 0.83 0.86 0.10 -0.38∗∗∗ -0.25∗∗∗ (0.68) (0.67) (0.30) (0.06) (0.04) Top x Crisis 1.80∗∗ 1.76∗∗ -0.05 -0.28∗∗∗ -0.21∗∗∗ (0.71) (0.71) (0.36) (0.06) (0.05) Top x SCAP 1.25 1.32 -2.21∗∗∗ -0.34∗∗∗ -0.28∗∗∗ (0.80) (0.81) (0.57) (0.07) (0.05) Top x Dodd-Frank 2.01∗∗ 1.84∗∗ -1.91∗∗∗ -0.35∗∗∗ -0.25∗∗∗ (0.79) (0.79) (0.46) (0.06) (0.04) Bank x Top x GLB -4.13∗∗∗ -4.69∗∗∗ 1.43∗∗ -0.07 0.16∗∗∗ (0.92) (0.92) (0.57) (0.09) (0.04) Bank x Top x Crisis -3.93∗∗∗ -5.06∗∗∗ 2.99∗∗∗ -0.26∗∗∗ 0.09 (1.05) (1.06) (0.76) (0.09) (0.06) Bank x Top x SCAP -0.95 -2.16 12.60∗∗∗ 0.04 0.26∗∗∗ (1.34) (1.44) (1.78) (0.11) (0.06) Bank x Top x Dodd-Frank -3.98∗∗∗ -5.10∗∗∗ 5.92∗∗∗ -0.25∗∗∗ 0.12∗∗ (1.33) (1.33) (1.14) (0.08) (0.05) Observations 1111062 1111062 1111062 1111062 1072888 1072888 1111062 1111062 890356 890356 Adjusted R2 0.491 0.494 0.413 0.416 0.671 0.675 0.460 0.471 0.656 0.663 Fixed Effects Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Weighting VW VW VW VW VW VW VW VW VW VW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms Table 9: Weighted Average Cost of Capital Estimates for Banks This table reports the differential weighted average cost of capital net of the risk-free rate (WACC- Rf) for banks over time relative to other industries and for the largest banks over time relative to large firms in other industries. Regressions are value-weighted by market capitalization or equal- weighted with some specifications including firm fixed effects. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) WACC-Rf WACC-Rf WACC-Rf WACC-Rf WACC-Rf WACC-Rf WACC-Rf GLB -0.02 -0.11 -0.63∗∗ 1.48∗∗∗ 0.77∗∗∗ 1.33∗∗∗ 0.91∗∗∗ (0.22) (0.24) (0.25) (0.18) (0.17) (0.21) (0.20) Crisis 0.62∗∗ 0.38 -0.30 1.93∗∗∗ 1.08∗∗∗ 3.00∗∗∗ 2.18∗∗∗ (0.27) (0.26) (0.27) (0.22) (0.19) (0.13) (0.14) SCAP 0.86∗∗∗ 0.55∗ -0.21 2.39∗∗∗ 1.60∗∗∗ 3.83∗∗∗ 3.00∗∗∗ (0.29) (0.29) (0.29) (0.22) (0.21) (0.16) (0.18) Dodd-Frank 0.93∗∗∗ 0.68∗∗∗ -0.35 2.30∗∗∗ 1.33∗∗∗ 3.85∗∗∗ 2.99∗∗∗ (0.27) (0.26) (0.27) (0.19) (0.20) (0.12) (0.14) Bank -5.94∗∗∗ -2.16∗∗∗ -5.54∗∗∗ -0.86∗ -4.87∗∗∗ -0.54 (0.25) (0.42) (0.30) (0.45) (0.11) (0.46) Bank x GLB 1.11∗∗∗ 1.00∗∗∗ 0.26 0.07 -0.28 0.07 (0.39) (0.30) (0.62) (0.23) (0.22) (0.18) Bank x Crisis 1.30∗∗ 1.34∗∗∗ 0.54 0.56 -1.14∗∗∗ -0.29 (0.53) (0.41) (1.08) (0.43) (0.33) (0.33) Bank x SCAP 2.54∗∗∗ 2.51∗∗∗ 1.57 1.33∗∗∗ -0.65∗∗∗ 0.18 (0.51) (0.39) (1.20) (0.30) (0.19) (0.20) Bank x Dodd-Frank 1.56∗∗∗ 1.66∗∗∗ 0.43 0.66∗∗∗ -1.35∗∗∗ -0.53∗∗∗ (0.42) (0.32) (0.59) (0.25) (0.13) (0.14) Top 0.77∗∗ 1.48∗∗∗ 1.05∗∗∗ 1.07∗∗∗ (0.34) (0.38) (0.18) (0.22) Bank x Top -0.54 -1.67∗∗∗ 0.13 -1.14∗∗∗ (0.42) (0.43) (0.20) (0.31) Top x GLB -2.27∗∗∗ -1.91∗∗∗ -1.31∗∗∗ -1.27∗∗∗ (0.35) (0.35) (0.19) (0.19) Top x Crisis -2.23∗∗∗ -1.86∗∗∗ -1.83∗∗∗ -1.64∗∗∗ (0.43) (0.39) (0.24) (0.24) Top x SCAP -2.60∗∗∗ -2.45∗∗∗ -1.88∗∗∗ -1.70∗∗∗ (0.45) (0.41) (0.26) (0.27) Top x Dodd-Frank -2.31∗∗∗ -2.25∗∗∗ -1.93∗∗∗ -1.96∗∗∗ (0.40) (0.38) (0.22) (0.23) Bank x Top x GLB 1.12 1.22∗∗∗ 0.87∗∗∗ 0.43∗∗ (0.71) (0.38) (0.30) (0.22) Bank x Top x Crisis 1.13 1.06∗∗ 1.67∗∗∗ 0.91∗∗∗ (1.14) (0.49) (0.42) (0.27) Bank x Top x SCAP 1.49 1.64∗∗∗ 2.04∗∗∗ 0.89∗∗ (1.30) (0.51) (0.56) (0.37) Bank x Top x Dodd-Frank 1.63∗∗ 1.37∗∗∗ 1.87∗∗∗ 0.68∗∗ (0.75) (0.43) (0.45) (0.28) Observations 649688 649688 649606 649688 649606 649688 649606 Adjusted R2 0.018 0.230 0.666 0.267 0.673 0.392 0.695 Fixed Eﬀects No No Yes No Yes No Yes Weighting VW VW VW VW VW EW EW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms

50 Figure 1: The Cost of Capital for Banks

This ﬁgure plots the CAPM cost of capital for banks in the CRSP-Compustat universe value- weighted by market capitalization from March 1996 to December 2017. The cost of capital is estimated for each bank as Et[Ri,t+1] = Rf,t + βi,t · µ where Rf,t is the three-month Treasury bill rate, βi,t is a time-varying beta from rolling one-year regressions of daily ﬁrm level excess returns onto CRSP value-weighted excess returns, and µ = 8.2% is the average annualized return for the CRSP value-weighted portfolio from 1975 to 2016.

51 Figure 2: The Cost of Capital for Banks Compared to Other Industries

This figure plots the difference in the CAPM cost of capital estimate net of the risk-free rate for banks and top banks relative to other firms in the CRSP-Compustat universe value-weighted by market capitalization from March 1996 to December 2017. The dashed lines plot the average differences across subperiods.

52 Figure 3: The Cost of Capital for the Largest Banks

This ﬁgure plots the CAPM cost of capital for the SCAP , CCAR, and other Top 90 largest banks by assets in the CRSP-Compustat universe as an equal-weighted average from March 1996 to December 2017. Table6 analyzes the cost of capital for these banks to study the impact of stress testing.

53 Figure 4: Senior Loan Oﬃcer Opinion Survey and Cost of Capital

This figure plots the average three-month change in credit standards for large and middle-market firms as measured by survey responses against the average one-year change in the CAPM risk premium from March 1996 to December 2017. In aggregate, changes in credit standards are 29% [1.83] correlated with the change in the CAPM risk premium, measuring significance with a Newey- West t-statistic in brackets that is computed with 4 quarterly lags. Gray bars indicate NBER recession shading.

54 Figure 5: Alternative Cost of Capital Estimates for Banks

The top ﬁgure plots the alternative cost of capital estimates in the CAPM, FF3, IR, and PLS models. The bottom ﬁgure plots asset beta against market leverage. The results are value-weighted by market capitalization for banks in the CRSP-Compustat universe from March 1996 to December 2017, except for the PLS model which is available until 2016.

55 A Appendix

A.1 Alternative deﬁnitions of regulatory breaks

In addition to varying our regulatory time periods by a few months, we experiment with different time series breaks. Because the SCAP was a one time stress test rather than a regulatory change, Table A.1 reports the results combining the Crisis and SCAP periods into a single Crisis period. Using these definitions, specifications (2) and (3) indicate that banks differential cost of capital declined by approximately 150 basis points from the combined Crisis period to the Dodd-Frank period, a result that remains economically and statistically significant. In comparison, specifications (2) and (3) in Table3 feature a significant decline of 450 basis points from SCAP to Dodd-Frank for banks but an insignificant decline from the Crisis to Dodd-Frank. Taken together these results reflect how banks CAPM betas increased significantly during the SCAP period from May 2009 to June 2010. This timing is in part a feature of our estimation approach that uses rolling one-year regressions with lagged data to estimate betas, indicating that bank betas were increasing the most during the fall of the financial crisis and in the ensuing months. Similarly, there continues to be a differential decline in the cost of capital for the very largest banks from the combined Crisis period to Dodd-Frank but with a smaller magnitude than before.

A.2 Alternative bank sample

To understand the robustness of our results to the definition of banks, Table A.2 reports the main difference-in-differences regressions defining banks as those firms whose two-digit SIC code is 60 (depository institutions). These regressions drop firms that were previously identified as banks but had SIC codes that did not begin with 60, since these firms are also subject to changes in bank regulation and thus do not belong in the comparison group. Results are generally similar to those presented in the paper, suggesting that the results are not sensitive to the definition of banks and that the changes to banks’ cost of capital are not being driven solely by changes to the sample of regulated banks.

A.3 Alternative beta estimation methods

In addition to exploring alternative factor models to the CAPM, we also check the robustness of our findings by varying the estimation method for computing time-varying betas. Table A.3 summarizes these results by reporting value-weighted difference-in-difference regressions for the CAPM, three-factor, and five-factor models using different estimation methods to

56 compute the betas for each of these models. In unreported analysis we confirm that similar results hold for specifications that include firm fixed effects. Overall we find that the cost of capital estimates are similar across the different beta estimation methods. In the first column (1) we report the baseline approach in which lagged betas are estimated from rolling regressions using daily returns over a one-year window. The second column (2) repeats this analysis using rolling regressions with overlapping weekly returns instead of daily returns. The third column (3) follows Ang and Kristensen(2012) to estimate centered betas from rolling Gaussian kernel-weighted regressions with an optimal bandwidth parameter that is selected for daily returns. The fourth column (4) estimates lagged betas following the betting-against-beta approach from Frazzini and Pedersen(2014) for the CAPM. Comparing the betas estimated from daily versus weekly returns, the betas from daily returns should be preferred in the absence of microstructure noise as the accuracy of co- variance estimation is increasing in the sampling frequency (Merton 1980). However, in the presence of noise such as nonsynchronous observations of firm-level and factor returns, zooming out to a lower frequency may be preferred. Empirically, we find the results are similar using betas estimated from daily and weekly returns. For example, the CAPM risk premium declines by 4.67% using daily betas and 4.07% using weekly betas from the SCAP to the Dodd-Frank period while increasing 1.89% and 1.32% relative to the pre-GLB period. The standard errors on these coefficients are about .50% to 1%, so these differences are not statistically significant. There is a difference, however, for the weekly beta estimates in the SCAP period where banks cost of capital appears somewhat lower in column (2) relative to column (1). In this case, one might argue in favor of the daily betas on economic grounds, as weekly returns during the financial crisis may be smoothing over some of the volatile moves in bank stocks that were correlated with the risk factors at daily and higher frequencies. In column (3) the Ang and Kristensen(2012) estimates (AK) differ from the other measures as they reflect centered betas that are smoothed in Gaussian kernel-weighted regressions.19 Despite these differences, the results are relatively similar across the different models. For example, in the case of the CAPM, the AK risk premium declined by 2.65% from SCAP to Dodd-Frank. While this magnitude is somewhat lower than in columns (1) and (2), the

19The optimal bandwidth balances the bias-variance trade-oﬀ in estimating the time-varying betas. It is estimated from a ﬁrst-stage regression using a uniform one-sided kernel with 252 days of lagged data (the baseline estimates). The distribution of optimal bandwidths for the second-stage regressions has a 1.96 z-score for the Gaussian kernel at .47, .88, 1.01, 1.12, and 1.48 years for the 1st, 25th, 50th, 75th, and 99th quantiles respectively. As a result, most of the weight for the kernel regressions falls within one-year of the current date. In rare cases where the 1.96 z-score is less than 3-months, we truncate the optimal bandwidth to ensure that at least 6-monthns of data fall within 95% of the mass for the Gaussian kernel. The truncation impacts less than .01% of observations.

57 AK estimates also feature a higher cost of capital for banks in the Crisis period relative to the daily and weekly betas. The CAPM risk premium for banks increases by 3.5% in column (3) versus only 1.87% and .90% increases in columns (1) and (2). Taken together, these differences reflect how the centered AK betas have shifted and smoothed some of the differential increase in the cost of capital for banks. Finally, in column (4), the betting-against-beta approach separates the estimation of the firm-level volatility and correlation parameters for the CAPM. Following Frazzini and Pedersen(2014), volatility is estimated using daily log-returns over the past year while correlation with the market is estimated using three-day log returns over the past five years. The results are similar to the estimates in columns (1) and (2), with the different treatment of the volatility and correlation parameters reflecting the tradeoffs in using daily versus weekly data as discussed above.

A.4 Additional Time-Varying Bank Characteristic Analysis

RWA is a complicated metric which makes it difficult to interpret the change in the bank x time interaction coefficients between column (2) and column (7) in Table5. Table A.4 extends the analysis by decomposing RWA into its component parts to better understand which type of risks are driving changes in the cost of capital over time. We examine the relationship between the cost of capital and securities (including cash, available-for-sale and held-to-maturity securities, and securities purchased under agreements to resell), loans, trading assets, loan commitments, and total derivatives. As before, we first include all of the variables unconditionally, then one by one conditionally, and then all conditionally with time-varying coefficients. While none of the RWA components by itself reverses the general patterns, we do find, as in Table5 specification (7), that including all RWA components results in no significant change for banks’ cost of capital from the SCAP to the Dodd-Frank periods. In addition, from inspecting the coefficients for the different components, we find evidence that loans and loan commitments drive part of the increase in RWA’s explanatory power during the SCAP period, although not enough to explain all of the change in banks’ cost of capital following the financial crisis. This contrasts securities, trading, and derivatives whose coefficients are roughly stable since the GLB period. Finally, we extend the analysis from Table5 for the largest banks by adding the bank x Top interaction terms. In these regressions we find a decline in the largest banks’ cost of capital by about 3% to 4% from the SCAP to the Dodd-Frank period across specifications, even with the increased coefficient on RWA during the SCAP period in specification (7). This indicates that RWA is not driving the results for the very largest banks, a result that contrasts Tables5 and A.4. Appendix Table 1: Cost of Capital Estimates for Banks with Alternative Regulatory Breaks This table reports the differential cost of capital for banks over time relative to other industries by regressing the CAPM expected return in annualized percentage units onto a constant and time period dummies along with indicator and interaction terms for banks. This table combines the Crisis and SCAP time periods to create one dummy for both periods. Regressions are value-weighted by market capitalization or equal-weighted with some specifications including firm fixed effects. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf GLB -0.22 -0.12 -0.84∗∗∗ -1.80∗∗∗ 1.37∗∗∗ 0.74∗∗∗ 1.49∗∗∗ 0.60∗∗∗ -0.34 1.43∗∗∗ 0.81∗∗∗ (0.18) (0.20) (0.20) (0.44) (0.21) (0.20) (0.23) (0.19) (0.27) (0.21) (0.21) Crisis 0.06 -0.26 -0.84∗∗∗ 0.99∗∗ 2.67∗∗∗ 1.69∗∗∗ 1.04∗∗∗ 0.32 1.31∗∗∗ 2.72∗∗∗ 1.73∗∗∗ (0.23) (0.23) (0.26) (0.46) (0.18) (0.18) (0.25) (0.25) (0.44) (0.18) (0.19) Dodd-Frank -0.09 -0.26 -0.98∗∗∗ -0.08 3.41∗∗∗ 2.18∗∗∗ 1.22∗∗∗ 0.38∗ 0.60∗ 3.53∗∗∗ 2.29∗∗∗ (0.20) (0.22) (0.25) (0.43) (0.15) (0.16) (0.22) (0.23) (0.35) (0.16) (0.17) Bank 0.65∗ -2.81∗∗∗ -2.84∗∗∗ -2.34∗∗∗ -2.29∗∗∗ -1.20∗∗∗ -2.68∗∗∗ -2.81∗∗∗ -2.50∗∗∗ -1.76∗∗∗ (0.37) (0.42) (0.46) (0.18) (0.54) (0.40) (0.50) (0.50) (0.17) (0.56) Bank x GLB -1.02∗∗ -0.58 0.38 -1.13∗∗∗ 0.33 -0.95∗ -0.06 0.89∗∗ -1.08∗∗∗ 0.40∗ (0.44) (0.40) (0.54) (0.21) (0.24) (0.50) (0.36) (0.38) (0.22) (0.24) Bank x Crisis 3.52∗∗∗ 3.81∗∗∗ 1.98∗∗∗ -0.03 2.14∗∗∗ 2.19∗∗∗ 3.35∗∗∗ 2.38∗∗∗ -0.11 2.15∗∗∗ (0.64) (0.70) (0.62) (0.29) (0.31) (0.61) (0.53) (0.57) (0.29) (0.32) Bank x Dodd-Frank 1.89∗∗∗ 2.32∗∗∗ 1.40∗∗ -0.42∗ 1.75∗∗∗ 1.69∗∗∗ 3.16∗∗∗ 2.98∗∗∗ -0.52∗∗ 1.81∗∗∗ (0.45) (0.51) (0.59) (0.25) (0.27) (0.46) (0.39) (0.44) (0.25) (0.27) 59 Top 0.46 1.24∗∗∗ 1.26∗∗ 1.71∗∗∗ 1.10∗∗∗ (0.31) (0.43) (0.63) (0.19) (0.26) Bank x Top 3.17∗∗∗ 0.20 0.16 5.19∗∗∗ 0.43 (0.53) (0.58) (0.69) (0.30) (0.52) Top x GLB -2.50∗∗∗ -2.13∗∗∗ -2.72∗∗∗ -1.46∗∗∗ -1.17∗∗∗ (0.41) (0.34) (0.69) (0.26) (0.25) Top x Crisis -2.02∗∗∗ -1.68∗∗∗ -0.17 -1.29∗∗∗ -0.70∗∗ (0.40) (0.40) (0.70) (0.28) (0.29) Top x Dodd-Frank -2.28∗∗∗ -1.94∗∗∗ -1.01 -2.26∗∗∗ -1.48∗∗∗ (0.36) (0.37) (0.72) (0.26) (0.27) Bank x Top x GLB -0.48 -0.97∗ -0.37 -1.27∗∗∗ -2.33∗∗∗ (0.71) (0.54) (0.81) (0.38) (0.39) Bank x Top x Crisis 1.18 0.33 -1.19 1.83∗∗∗ 0.05 (0.82) (0.78) (0.86) (0.62) (0.60) Bank x Top x Dodd-Frank -0.23 -1.31∗∗ -2.29∗∗∗ 0.25 -1.94∗∗∗ (0.66) (0.61) (0.88) (0.50) (0.51) Observations 1111127 1111127 1111062 223432 1111127 1111062 1111127 1111062 223432 1111127 1111062 Adjusted R2 0.001 0.033 0.536 0.535 0.103 0.536 0.086 0.545 0.557 0.110 0.537 Fixed Effects No No Yes Yes No Yes No Yes Yes No Yes Weighting VW VW VW VW EW EW VW VW VW EW EW Sample All Firms All Firms All Firms Banks+NBF All Firms All Firms All Firms All Firms Banks+NBF All Firms All Firms Appendix Table 2: Cost of Capital Estimates for Banks with Alternative Bank Sample This table reports the differential cost of capital for banks over time relative to other industries by regressing the CAPM expected return in annualized percentage units onto a constant and time period dummies along with indicator and interaction terms for banks. This table uses an alternative definition of banks defined as SIC code 60 firms and removing from the panel banks in the original sample that don’t have SIC code 60. Regressions are value-weighted by market capitalization or equal-weighted with some specifications including firm fixed effects. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf CAPM - Rf GLB -0.24 -0.12 -0.83∗∗∗ -1.76∗∗∗ 1.37∗∗∗ 0.74∗∗∗ 1.50∗∗∗ 0.61∗∗∗ -0.22 1.43∗∗∗ 0.81∗∗∗ (0.18) (0.20) (0.20) (0.47) (0.21) (0.20) (0.23) (0.20) (0.27) (0.21) (0.21) Crisis -0.14 -0.26 -0.85∗∗∗ 0.62 2.38∗∗∗ 1.44∗∗∗ 0.94∗∗∗ 0.24 1.22∗∗∗ 2.43∗∗∗ 1.49∗∗∗ (0.21) (0.23) (0.26) (0.46) (0.18) (0.19) (0.26) (0.26) (0.45) (0.19) (0.21) SCAP 0.18 -0.28 -0.81∗∗∗ 2.80∗∗∗ 3.29∗∗∗ 2.23∗∗∗ 1.28∗∗∗ 0.53∗∗ 2.53∗∗∗ 3.34∗∗∗ 2.26∗∗∗ (0.30) (0.25) (0.29) (0.76) (0.19) (0.20) (0.26) (0.27) (0.53) (0.20) (0.21) Dodd-Frank -0.16 -0.27 -0.98∗∗∗ 0.11 3.41∗∗∗ 2.20∗∗∗ 1.23∗∗∗ 0.40∗ 0.69∗∗ 3.53∗∗∗ 2.31∗∗∗ (0.21) (0.22) (0.25) (0.46) (0.15) (0.16) (0.22) (0.23) (0.35) (0.16) (0.17) Bank 0.52 -3.14 -11.01∗∗∗ -2.33∗∗∗ -2.25∗∗∗ -1.20∗∗∗ -3.35∗ -11.25∗∗∗ -2.49∗∗∗ -2.23∗∗∗ (0.37) (2.07) (1.69) (0.17) (0.81) (0.40) (1.90) (1.50) (0.17) (0.82) Bank x GLB -1.36∗∗∗ -0.49 0.43 -1.17∗∗∗ 0.32 -1.38∗∗∗ -0.24 0.57∗ -1.10∗∗∗ 0.38 (0.40) (0.40) (0.58) (0.21) (0.23) (0.33) (0.33) (0.35) (0.22) (0.24) Bank x Crisis 1.73∗∗∗ 2.56∗∗∗ 1.09∗∗ -0.08 2.03∗∗∗ 1.24∗∗ 3.11∗∗∗ 2.12∗∗∗ -0.08 2.06∗∗∗ (0.58) (0.62) (0.55) (0.30) (0.33) (0.51) (0.50) (0.55) (0.30) (0.34) 60 Bank x SCAP 6.02∗∗∗ 6.85∗∗∗ 3.24∗∗∗ -0.10 2.27∗∗∗ 1.66∗∗ 3.90∗∗∗ 1.89∗∗ -0.16 2.24∗∗∗ (1.04) (1.05) (1.14) (0.32) (0.33) (0.69) (0.69) (0.79) (0.32) (0.34) Bank x Dodd-Frank 1.50∗∗∗ 2.67∗∗∗ 1.58∗∗ -0.56∗∗ 1.73∗∗∗ 1.19∗∗∗ 3.25∗∗∗ 2.95∗∗∗ -0.59∗∗ 1.75∗∗∗ (0.44) (0.61) (0.71) (0.25) (0.27) (0.45) (0.39) (0.46) (0.25) (0.27) Top 0.46 1.26∗∗∗ 1.05 1.71∗∗∗ 1.09∗∗∗ (0.31) (0.44) (0.72) (0.19) (0.26) Bank x Top 3.02∗∗∗ 0.33 0.57 5.14∗∗∗ 0.75 (0.53) (0.64) (0.86) (0.30) (0.60) Top x GLB -2.50∗∗∗ -2.13∗∗∗ -2.89∗∗∗ -1.46∗∗∗ -1.17∗∗∗ (0.41) (0.34) (0.73) (0.26) (0.25) Top x Crisis -1.86∗∗∗ -1.58∗∗∗ -0.95 -1.35∗∗∗ -0.83∗∗∗ (0.42) (0.41) (0.74) (0.29) (0.31) Top x SCAP -2.37∗∗∗ -1.93∗∗∗ 1.67 -1.23∗∗∗ -0.49 (0.42) (0.45) (1.41) (0.36) (0.35) Top x Dodd-Frank -2.29∗∗∗ -1.95∗∗∗ -0.58 -2.26∗∗∗ -1.47∗∗∗ (0.36) (0.37) (0.85) (0.26) (0.28) Bank x Top x GLB -0.33 -0.64 0.13 -1.34∗∗∗ -2.28∗∗∗ (0.62) (0.55) (0.84) (0.39) (0.40) Bank x Top x Crisis 0.19 -1.01∗ -1.63∗∗ 0.54 -0.80 (0.69) (0.59) (0.80) (0.61) (0.64) Bank x Top x SCAP 5.59∗∗∗ 3.86∗∗∗ 0.26 4.19∗∗∗ 2.38∗∗ (1.16) (1.25) (1.78) (0.97) (1.00) Bank x Top x Dodd-Frank 0.08 -1.12 -2.48∗∗ 0.07 -1.59∗∗∗ (0.69) (0.69) (1.03) (0.51) (0.58) Observations 1108439 1108439 1108374 220744 1108439 1108374 1108439 1108374 220744 1108439 1108374 Adjusted R2 0.001 0.025 0.538 0.577 0.105 0.537 0.081 0.548 0.607 0.111 0.538 Fixed Effects No No Yes Yes No Yes No Yes Yes No Yes Weighting VW VW VW VW EW EW VW VW VW EW EW Sample All Firms All Firms All Firms Banks+NBF All Firms All Firms All Firms All Firms Banks+NBF All Firms All Firms Appendix Table 3: Cost of Capital Estimates for Banks with Alternative Betas This table reports the differential cost of capital for banks relative to other industries for the CAPM, three-factor, and five-factor models using different estimation methods to compute time-varying betas. Daily and weekly returns over the past year are used to compute lagged betas from rolling regressions (Daily and Weekly columns). Daily returns are also used to compute centered betas following the Ang and Kristensen(2012) approach (AK) and lagged betas following the betting-against-beta approach (BAB) from Frazzini and Pedersen (2014). Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels.

CAPM-Rf FF3-Rf IR-Rf (1) (2) (3) (4) (1) (2) (3) (1) (2) (3) Daily Weekly AK BAB Daily Weekly AK Daily Weekly AK GLB -0.12 -0.02 0.30 -0.51∗∗ 0.84∗∗ 0.97∗∗ 0.58∗ 0.69∗∗ 0.77∗∗ 0.42 (0.20) (0.21) (0.21) (0.22) (0.35) (0.40) (0.33) (0.34) (0.38) (0.34) Crisis -0.26 -0.20 0.04 -1.06∗∗∗ 0.25 0.30 0.44 0.34 0.30 0.74∗ (0.23) (0.22) (0.23) (0.23) (0.43) (0.44) (0.42) (0.42) (0.44) (0.42) SCAP -0.28 -0.01 -0.13 -0.80∗∗∗ 0.76 1.04∗∗ 0.48 0.88∗ 1.37∗∗∗ 0.62 (0.25) (0.25) (0.25) (0.26) (0.47) (0.51) (0.43) (0.47) (0.53) (0.45) Dodd-Frank -0.26 -0.17 -0.03 -0.70∗∗∗ 0.42 0.49 0.32 0.70 0.83 0.72 (0.22) (0.19) (0.22) (0.21) (0.48) (0.51) (0.44) (0.48) (0.52) (0.46) Bank 0.65∗ 1.22∗∗∗ 0.92∗∗ 0.95∗∗∗ 8.95∗∗∗ 9.00∗∗∗ 8.53∗∗∗ 9.01∗∗∗ 8.90∗∗∗ 8.88∗∗∗ 61 (0.37) (0.36) (0.36) (0.36) (0.67) (0.71) (0.65) (0.67) (0.74) (0.62) Bank x GLB -1.02∗∗ -1.91∗∗∗ -1.39∗∗∗ -1.60∗∗∗ -7.48∗∗∗ -7.96∗∗∗ -7.01∗∗∗ -6.27∗∗∗ -6.52∗∗∗ -6.10∗∗∗ (0.44) (0.45) (0.47) (0.46) (0.66) (0.68) (0.63) (0.63) (0.73) (0.56) Bank x Crisis 1.87∗∗∗ 0.90 3.53∗∗∗ 1.41∗∗ -0.81 -1.36 1.90∗∗ -0.80 -0.55 0.97 (0.60) (0.61) (0.55) (0.62) (0.95) (0.97) (0.88) (0.88) (0.99) (0.72) Bank x SCAP 6.56∗∗∗ 5.39∗∗∗ 4.37∗∗∗ 5.86∗∗∗ -1.01 -3.12∗∗∗ -2.07∗∗ -1.07 -4.93∗∗∗ -2.00∗∗ (0.87) (1.22) (0.75) (0.92) (0.98) (1.08) (0.86) (1.01) (1.24) (0.98) Bank x Dodd-Frank 1.89∗∗∗ 1.32∗∗∗ 1.72∗∗∗ 1.53∗∗∗ -1.71∗∗ -2.11∗∗ -1.01 -4.78∗∗∗ -6.03∗∗∗ -4.63∗∗∗ (0.45) (0.48) (0.47) (0.46) (0.86) (0.87) (0.90) (0.88) (1.02) (0.90) Observations 1110835 1110835 1110835 1110835 1110835 1110835 1110835 1110835 1110835 1110835 Adjusted R2 0.039 0.029 0.041 0.036 0.099 0.070 0.121 0.067 0.033 0.086 Fixed Effects No No No No No No No No No No Weighting VW VW VW VW VW VW VW VW VW VW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms Appendix Table 4: The Cost of Capital Controlling for Components of Risk-Weighted Assets This table reports the differential cost of capital for banks over time relative to other industries controlling for components of risk-weighted assets. Regulatory variables are obtained from call reports and Y-9C filings. The results are reported for expected excess returns in the CAPM in value-weighted regressions with firm fixed effects. The time period dummies and bank indicator are included in the regressions but omitted in the results for brevity. Column (1) replicates column (8) from Table3. Column (2) includes all of the characteristics unconditionally. Columns (3) to (7) allow the coefficients on each characteristic to vary over time through interaction terms. Column (8) includes all of the characteristics together with time-varying coefficients. Standard errors are clustered by firm and month with ∗, ∗∗, ∗∗∗ indicating significance at the 10%, 5%, and 1% levels. The sample period is March 1996 to December 2017.

(1) (2) (3) (4) (5) (6) (7) (8) None All Cash+FF+Sec. Loans Trading Assets Commitments Derivatives All Bank x GLB -0.58 -0.50 -1.48∗∗∗ -0.87∗ -0.17 -0.44 -0.21 -0.79∗ (0.40) (0.39) (0.43) (0.52) (0.41) (0.41) (0.38) (0.44) Bank x Crisis 2.24∗∗∗ 2.29∗∗∗ 1.70∗∗ 1.25 2.97∗∗∗ 3.15∗∗∗ 2.72∗∗∗ 1.80∗∗ (0.65) (0.64) (0.75) (0.82) (0.60) (0.55) (0.62) (0.75) Bank x SCAP 6.88∗∗∗ 6.92∗∗∗ 7.11∗∗∗ 3.56∗∗∗ 7.60∗∗∗ 5.54∗∗∗ 7.30∗∗∗ 2.15 (0.95) (0.94) (1.64) (1.33) (1.08) (1.11) (1.03) (1.54) 62 Bank x Dodd-Frank 2.45∗∗∗ 2.52∗∗∗ 2.72∗∗∗ 0.60 2.98∗∗∗ 2.13∗∗∗ 2.87∗∗∗ 0.98 (0.53) (0.51) (0.66) (1.15) (0.55) (0.68) (0.51) (1.40) Characteristic -0.05∗∗∗ -0.02 0.11∗∗ -0.01 0.13∗∗∗ (0.02) (0.01) (0.05) (0.01) (0.03) Characteristic x GLB 0.03∗∗ 0.00 -0.09∗∗ -0.00 -0.11∗∗ (0.01) (0.01) (0.04) (0.00) (0.04) Characteristic x Crisis 0.02 0.02 -0.13∗∗∗ -0.02∗∗ -0.12∗∗∗ (0.02) (0.01) (0.03) (0.01) (0.02) Characteristic x SCAP -0.00 0.07∗∗∗ -0.12∗∗ 0.03∗∗ -0.11∗∗∗ (0.04) (0.02) (0.05) (0.01) (0.03) Characteristic x Dodd-Frank 0.00 0.03∗∗ -0.11∗∗ 0.01 -0.11∗∗∗ (0.02) (0.02) (0.05) (0.01) (0.02) Observations 1111062 1111062 1111062 1111062 1111062 1111062 1111062 1111062 Adjusted R2 0.542 0.542 0.543 0.543 0.542 0.543 0.542 0.545 Fixed Effects Yes Yes Yes Yes Yes Yes Yes Yes Weighting VW VW VW VW VW VW VW VW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms Characteristic None All Cash+FF+Sec. Loans Trading Assets Commitments Derivatives All Time Varying NA No Yes Yes Yes Yes Yes Yes Appendix Table 5: The Cost of Capital for Top Banks Controlling for Bank Characteristics This table reports the differential cost of capital for banks and for the largest banks over time relative to other industries and to the largest firms in other industries by adding the Bank x Top interaction terms to the regressions in Table5 that control for time-varying bank characteristics. As before, we omit the time period dummies and Bank and Top indicators and interactions for brevity.

(1) (2) (3) (4) (5) (6) (7) (8) None All Non Int. Inc. Core Deposits Liq. Coverage Tier 1 RWA All Bank x GLB -0.03 -0.17 0.29 -0.97∗∗ -0.48 -0.37 -0.06 -0.60 (0.36) (0.33) (0.44) (0.48) (0.34) (0.38) (0.39) (0.40) Bank x Crisis 3.02∗∗∗ 2.87∗∗∗ 3.97∗∗∗ 1.31∗∗ 1.35∗ 2.63∗∗∗ 2.36∗∗∗ 1.72∗∗ (0.53) (0.52) (0.62) (0.64) (0.69) (0.57) (0.79) (0.71) Bank x SCAP 4.42∗∗∗ 4.33∗∗∗ 5.29∗∗∗ 0.27 2.40∗∗ 4.35∗∗∗ -0.04 0.11 (0.64) (0.65) (0.87) (0.77) (1.11) (0.82) (1.14) (1.05) Bank x Dodd-Frank 3.25∗∗∗ 3.03∗∗∗ 4.20∗∗∗ 1.15∗ 1.68∗∗ 3.18∗∗∗ 2.17∗∗ 1.36 (0.39) (0.44) (0.52) (0.64) (0.79) (0.49) (0.85) (1.06) Bank x Top 0.13 0.11 -0.07 -0.06 0.14 0.14 0.06 -0.25 (0.60) (0.58) (0.57) (0.56) (0.59) (0.62) (0.56) (0.57) Bank x Top x GLB -0.99∗ -0.80 -0.81 -0.78 -0.97∗ -0.87 -0.92∗ -0.21 (0.55) (0.51) (0.54) (0.54) (0.54) (0.54) (0.55) (0.54) Bank x Top x Crisis -1.27∗ -1.06 -0.84 -0.97 -0.77 -1.15∗ -1.25∗ 0.49 (0.70) (0.66) (0.69) (0.64) (0.64) (0.67) (0.66) (0.61) 63 Bank x Top x SCAP 2.78∗∗∗ 2.78∗∗∗ 3.15∗∗∗ 3.67∗∗∗ 2.80∗∗∗ 2.73∗∗ 1.90∗∗ 3.23∗∗∗ (1.07) (1.03) (1.04) (0.88) (0.98) (1.08) (0.90) (1.04) Bank x Top x Dodd-Frank -1.24∗ -1.12∗ -0.74 -0.69 -1.08∗ -1.25∗ -1.17∗ -0.22 (0.63) (0.63) (0.64) (0.58) (0.59) (0.64) (0.64) (0.63) Characteristic 0.03∗∗∗ -0.06∗∗∗ -0.01 0.00 0.00 (0.01) (0.02) (0.02) (0.02) (0.01) Characteristic x GLB -0.01 0.02∗∗ 0.01∗∗∗ 0.02 -0.00 (0.01) (0.01) (0.00) (0.02) (0.00) Characteristic x Crisis -0.03∗∗∗ 0.04∗∗∗ 0.04∗∗∗ 0.03 0.01 (0.01) (0.01) (0.01) (0.02) (0.01) Characteristic x SCAP -0.03∗ 0.10∗∗∗ 0.05∗∗ 0.01 0.08∗∗∗ (0.02) (0.02) (0.02) (0.02) (0.02) Characteristic x Dodd-Frank -0.03∗∗∗ 0.05∗∗∗ 0.03∗∗ 0.00 0.01 (0.01) (0.01) (0.01) (0.02) (0.01) Observations 1111062 1111062 1111062 1111062 1111062 1111062 1111062 1111062 Adjusted R2 0.551 0.552 0.551 0.553 0.552 0.551 0.552 0.554 Fixed Eﬀects Yes Yes Yes Yes Yes Yes Yes Yes Weighting VW VW VW VW VW VW VW VW Sample All Firms All Firms All Firms All Firms All Firms All Firms All Firms All Firms Characteristic None All Non Int. Inc. Core Deposits Liq. Coverage Tier 1 RWA All Time Varying NA No Yes Yes Yes Yes Yes Yes